The Citizens earned their 18th successive top-flight win thanks to Raheem Sterling's first-half strike, which they were unable to add to despite dominating against a defensive home side.
City rattled the frame of the goal three times and also saw opposition keeper Rob Elliot pull off a couple of important saves, but one goal proved enough to move them further in front of second-placed Manchester United.
Newcastle's tactics were clear to see right from the off, putting all 10 outfield players behind the ball yet still giving City's main man Kevin De Bruyne plenty of room to operate in.
De Bruyne's quality did not take too long to shine through, though his shooting range was a little off as he sent two attempts over the bar from outside the box.
The upright came to Newcastle's rescue on those occasions but Elliot was also required, producing a big save to keep out the Argentina international's glanced header.
City were forced into a first-half change when skipper Vincent Kompany hobbled off, and the man who replaced him also saw a chance to open the scoring come and go, as Gabriel Jesus was thwarted by Elliot at his near post.
There was to be no keeping out Sterling soon after, however, with the in-form winger volleying past Elliot once picked out by a lofted De Bruyne pass for the match-winning moment.
A Jonjo Shelvey shot from kickoff aside, Newcastle did not impose themselves on the game until 34 minutes in when Rolando Aarons - handed his first Premier League start of the season - lobbed Ederson but saw the ball kept off the line by Nicolas Otamendi
Sterling curled one narrowly wide and Gundogan's tame shot was helped aside, while De Bruyne wasted his latest attempt from close range when played through by Jesus.
De Bruyne was a little more accurate with 66 minutes on the clock, though, sending a bullet strike cannoning back off the post, with Aguero flagged for offside from the successfully-converted rebound.
With a quarter of the match left to play, and still just the one goal between the sides, the Magpies offered a little more in an attacking sense.
Gayle also sent a header flying past Ederson's post in the final minute of normal time, with that proving to be the closest United came to ending a run of 20 Premier League games without a win in this fixture.