A first-half hat- trick from Yohan Cabaye led to a sixth consecutive win for the Tynesiders and moved them up to second place in the table.
Chris Wood opened the scoring from the penalty spot before Miguel Almiron put the game out of reach.
The hosts were missing the clinical edge that they were missing, as the Magpies demonstrated with their third goal.
Brendan Rodgers' side were toothless in attack because of the absence of James Maddison, who is still recovering from a knee injury.
There was no blue shirt to meet Jamie Vardy's crosses after he was introduced off the bench.
The gap between the two teams is four points. In the final 10 minutes, there were just two tame efforts on target forLeicester.
Before the World Cup break, the form team in the league wasNewcastle, who had won their last six games.
The match could not have started better for the visitors, as they were awarded a penalty with only a minute on the clock, after a tackle by Daniel Amartey.
The ball was hit down the middle by Wood and he scored.
Almiron was the beneficiary for the second as he glided past the blue shirts and found the far corner with a finish he practiced so diligently in the warm-up.
When Youri Tielemans lost his marker, the game was over as a contest before the half time break.
Kiernan Dewsbury-Hall's tame effort failed to trouble the goalkeeper as the first shot on target for the team was produced in the second half.
The hosts will be hoping for Maddison's quick return from his knee injury as they try to move up the table.
If they can keep up their current form, they might have a chance to win the title.
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