The 29-year-old surpassed former Spurs and England forward Jimmy Greaves, who had held the record since the late 1960s.
Here we list every Premier League club’s top scorer and their nearest present-day challenger.
Thierry Henry - 228
Henry scored 226 goals in eight seasons at Arsenal between 1999 and 2007, helping the club to two Premier League titles and two FA Cups.
He added a further two when on loan from the New York Red Bulls in 2011-12, ending his Gunners career with 228 goals in 377 appearances.
Eddie Nketiah is the highest scorer among Mikel Arteta’s current squad, with 32 from 119 matches in all competitions.
Billy Walker - 244
Walker scored 244 goals in 531 appearances for Villa between 1919 and 1933.
He assumed the goalscoring mantle at Villa Park from Harry Hampton, who set the benchmark at 242 in a 16-year period that immediately preceded Walker’s first-team debut.
Full-back Ashley Young leads the way among the current crop, having netted 39 Villa goals across two stints. All but one of Young’s total came in his first spell, when he was deployed as a winger.
Ron Eyre - 229
Eyre netted 229 times for the Cherries in the 1920s and 1930s, when the club was called Bournemouth and Boscombe Athletic.
Dominic Solanke is Bournemouth’s highest active scorer with 53, having celebrated 50 goals when scoring the equaliser in a 3-2 win at Nottingham Forest in September.
Jim Towers - 163
Towers racked up 163 goals in seven productive seasons at Griffin Park from 1954-55 to 1960-61.
He and strike partner George Francis - Brentford’s second-highest scorer with 136 - terrorised Third Division defences, with one newspaper describing the duo as ‘The Terrible Twins’.
Despite being well short of the record, Ivan Toney is keeping pace with Towers having netted 61 times in two and a half years so far.
Tommy Cook - 123
Cook enjoyed a remarkable sporting career on the south coast in the 1920s and 1930s.
As well as scoring a record 123 goals for Brighton, he accumulated more than 20,000 first-class runs for Sussex - which places him in the top 10 on their all-time list.
Cook’s haul was unofficially beaten by Bert Stephens, who played for the Seagulls between 1935 and 1948, but many of Stephens’ goals came in non-competitive wartime matches.
Centre-back Lewis Dunk is the highest-scoring current squad member, having netted his 26th goal in the recent FA Cup fourth-round win over Liverpool.
Frank Lampard - 211
Lampard’s recent struggles as a manager are in stark contrast to his stellar playing career, in which he won three Premier Leagues, a Champions League and four FA Cups with Chelsea.
He scored a club-record 211 goals from midfield, surpassing Bobby Tambling’s mark that had stood since the 1960s.
Mason Mount - promoted to the first-team by Lampard in his time as manager - is Chelsea’s highest present-day scorer, with 33 goals from 188 appearances.
Peter Simpson - 165
Simpson averaged nearly a goal per game in his six-year spell at Palace.
His most prolific season came in 1930-31, during which he scored 54 times in the league and FA Cup.
Wilfried Zaha is over halfway to Simpson’s total but he has played more than twice as many games (450 compared with 195). Zaha’s tally of 89 puts him 10th on the Palace all-time list.
Dixie Dean - 383
Arguably the greatest goalscorer on this list, Dean found the net 383 times in 433 games for Everton between 1925 and 1937.
Dean remains the only player in English football history to score 60 league goals in a single season - a feat he accomplished in 1927-28 as the Toffees lifted the First Division title.
Nobody else has managed even half of Dean’s overall tally for Everton, with Dominic Calvert-Lewin (59) leading the way among the current squad.
Gordon Davies - 178
Davies amassed 178 goals across two spells at Fulham, overtaking Johnny Haynes as the club’s record scorer.
Aleksandar Mitrovic is on track to overhaul Davies, however, having netted 107 goals in 196 games for the Cottagers.
The Serbian - who is already eighth on Fulham’s all-time list - would need another 132 matches to break the record at his current scoring rate.
Peter Lorimer - 238
Lorimer was a key part of a Leeds side that won two First Division titles and an FA Cup, before reaching a European Cup final in 1974-75.
Renowned for long-range strikes and firmly struck penalties, Lorimer scored his club-record 238 goals from midfield.
Patrick Bamford (48) is the top scorer among active players, despite suffering injury problems in recent seasons.
Arthur Chandler - 273
Chandler was 27 years old when he signed for Leicester in 1923, but he still went on to score 273 times in 13 years with the club.
Remarkably, none of Chandler’s goals came from the penalty spot, with the striker reportedly taking just two spot-kicks in his career - both of which he missed.
Jamie Vardy is third on the Foxes’ all-time list with 168 goals in 410 appearances. The 36-year-old has struggled so far this season, finding the net just four times in all competitions.
Ian Rush - 346
Rush led the line in an enormously successful era for Liverpool, helping the club to five top-flight titles, three FA Cups and two European Cups.
Mohamed Salah is climbing the Reds’ all-time list, having recently claimed seventh spot from Kenny Dalglish, but his tally of 173 goals is only halfway to matching Rush’s haul of 346.
Robbie Fowler and Steven Gerrard are next in Salah’s sights, on 183 and 186 respectively.
Sergio Aguero - 260
Aguero set the standard at City for a decade, scoring the goal that sealed the club’s first Premier League title in 2011-12 and going on to break more or less every scoring record.
His total of 260 goals is a long way clear of anybody in Pep Guardiola’s current squad, with Kevin De Bruyne the closest challenger on 89.
However, Erling Haaland’s prolific start to his City career - in which he has netted 31 times in 28 games - suggests that he could one day challenge Aguero’s mark.
Wayne Rooney - 253
Rooney overhauled Sir Bobby Charlton as top scorer for Manchester United in January 2017, just 16 months after taking his England record.
The former England captain scored 253 goals for the Red Devils over the course of 13 years, surpassing Charlton in his final season with the club.
While Kane has already equalled Rooney’s England mark, in-form Marcus Rashford (112) has a long way to go to reach his United tally.
Alan Shearer - 206
Shearer netted 206 goals in 10 seasons at Newcastle - the club he supported as a boy - breaking Jackie Milburn’s long-standing record just a few months before retiring.
He turned down Sir Alex Ferguson and Manchester United to sign for the Magpies in 1996, following four prolific years at Blackburn, and went on to become the Premier League’s all-time top scorer.
The latter record could soon be under threat from Kane but Shearer’s Newcastle mark is safe for now, with Callum Wilson (27) the closest to it among the current crop.
Grenville Morris - 217
Set more than 100 years ago, Nottingham Forest’s all-time scoring record has stood for longer than any other Premier League club.
Morris netted 217 times for Forest between 1898 and 1913, having arrived at the City Ground for a fee of £200.
Fellow Welshman Brennan Johnson is the highest scoring of Steve Cooper’s present-day squad, with 26 since his debut in 2019.
Mick Channon - 228
Channon edges out Matt Le Tissier (209) for the title of Southampton’s leading scorer.
The former England striker was part of a team that won the FA Cup in 1976 - the Saints’ biggest trophy to date - and later became a successful horse trainer.
Free-kick specialist James Ward-Prowse is Channon’s nearest modern-day challenger, having played for Southampton throughout his career so far and racked up 51 goals.
Harry Kane - 267
Kane became Tottenham’s greatest scorer with his goal in Sunday’s victory over Man City, having equalled Greaves’ record in his previous Premier League game against Fulham while playing with a fever.
The England captain had loan spells at Leyton Orient, Millwall, Norwich and Leicester before breaking into the Spurs first team in 2014-15, since which he has scored at least 20 goals in every completed season.
Vic Watson - 326
West Ham paid £50 to sign Watson from Wellingborough in 1920, a fee that he returned with interest during a 15-year career with the Hammers.
Watson’s total of 326 goals is 74 more than Sir Geoff Hurst managed in his time at Upton Park.
Michail Antonio - the top scorer in the current squad - trails both Watson and Hurst by some distance on 67 strikes.
Steve Bull - 306
Bull joined Wolves in 1986 when they were in the fourth tier and went on to score 306 goals in 561 appearances, eventually hanging up his boots in 1999 with the club challenging for promotion to the Premier League.
Despite never playing for Wolves in the top flight, he received 13 England caps in his time at Molineux.
Nobody else in the club’s history has passed 200 goals, with Raul Jimenez their highest active scorer on 57.