Coming into the contest a whopping 14 points off the PL summit, Man City started brightly during an entertaining opening 20 minutes.
Erling Haaland saw a low strike saved by the legs of Jakub Stolarczyk, while at the other end, Stefan Ortega dived bravely to thwart an angled effort from Jamie Vardy.
Guardiola’s side continued to threaten in the final third and it was the struggling visitors who broke the deadlock when Savinho lashed home from close range after Phil Foden’s initial effort was parried away by Stolarczyk – the Brazilian’s long-awaited first goal of the season.
The end-to-end nature of the match showed no signs of slowing down as the first half progressed, with Haaland dribbling past several defenders on the edge of the box, only to shoot narrowly wide of the target.
Leicester came within inches of an equaliser shortly after, as the recalled Facundo Buonanotte directed a close-range header agonisingly against the post.
The Foxes continued to probe for a leveller in the early stages of the second period, with Bilal El Khannouss curling over and James Justin seeing a flicked effort cleared off the line by Manuel Akanji.
As time ticked into the final 25 minutes, the hosts spurned another glorious opportunity to draw level when Vardy lifted wastefully over the bar from inside the six-yard box.
That miss proved to be crucial as Man City doubled their lead in the 74th minute through Haaland, who headed clinically into the far corner from Savinho’s delivery to spark wild celebrations in the away end.
From there, the Cityzens coasted through the closing stages to secure a first away win in six PL matches, while Ruud van Nistelrooy’s Leicester fall to a fourth successive defeat.