Newcastle climbed further away from the Premier League relegation zone with a third consecutive victory and their first at Turf Moor in more than 40 years.
Federico Fernandez scored the opener in the 2-1 victory in only the fourth minute via a big deflection off Ben Mee and Ciaran Clark, in for the injured Paul Dummett, made it two 19 minutes later.
Burnley pulled one back through a fine header from Sam Vokes five minutes before the break but were unable to find an equaliser and Sean Dyche's side remain just above the bottom three.
Newcastle would have won by more but for an extraordinary miss from Matt Ritchie while Joselu hit a post. PA
The Clarets put a three-game losing run, during which they conceded 13 goals, behind them by holding the Foxes to a goalless draw on an emotional afternoon as the King Power Stadium remembered late Leicester owner Vichai Srivaddhanaprabha.
Dyche said: "I thought the structure of the side was better. I thought it looked more like what we look like on a consistent level of performance. There's still more to come.
"I think we showed a lot of signs of continued belief in the growth, and literal growth in performances, last season, that's stuttered a bit at the beginning of this season, for many different reasons I feel.
"We know where the team is statistically and we know that still needs adjusting but, for the last number of weeks, we are showing signs of getting back to where we want to be. We know we still need to do more on the offensive side." (PA)

Kick-off delayed
