The England international struck a fine equaliser as the Reds held the champions 1-1 in a tight encounter at the Etihad Stadium on Saturday.
Erling Haaland had put City ahead with his 50th Premier League goal from just 48 appearances – a new record – but Alexander-Arnold, having come through some tough moments against the tricky Jeremy Doku, changed the script 10 minutes from time.
Having stepped into midfield, the 25-year-old took a touch and fired into the bottom corner from outside the area to peg back City and allow Arsenal, courtesy of their victory at Brentford, to take top spot.
It was a strong reminder of Alexander-Arnold’s talents after an international break in which there has been much debate over how he can be most effectively deployed by England manager Gareth Southgate.
Liverpool boss Klopp said: “Trent was super influential. Not only in the goal – around the goal, in all situations he was a really important player. He played a really good game.
“We changed it, with the position. We made it more clear where he has to be in these moments.
“He did that really well and had still his moments with Doku where he was really strong in the one-on-one situations.
“You could see in a lot of moments how difficult it is against him, he is a really good dribbler. Trent was pretty influential in a good way.”
Alexander-Arnold’s leveller not only took the gloss off Haaland’s achievement – the previous quickest player to a half-century was Andy Cole in 65 games – but also denied City a share of another record.
Pep Guardiola’s side had won their previous 23 home games in all competitions, stretching back to a draw against Everton last December, and another would have equalled Sunderland’s record for an English top-flight side set between 1890 and 1892.
City, however, were the most dominant side, racking up 16 attempts on goal to Liverpool’s eight and felt aggrieved when a Ruben Dias goal was ruled out for a foul on goalkeeper Alisson Becker, who had an afternoon to forget.
Alisson had been at fault for City’s opener, made numerous other mistakes in the game and picked up a hamstring injury late on.
City defender Nathan Ake said: “I think we wanted more. We felt OK, we felt solid. We didn’t create too many chances but I think we controlled the game way more than we did against Chelsea, which was more up and down.
“We tried to create some chances. Just before their goal we created a very good one.
“We know they have the quality where they can – suddenly out of nothing – score a goal but, in the end, it is frustrating that one shot from distance goes in and you draw the game.”