And a ninth successive Premier League triumph was then confirmed after the break as we moved three points clear of second-placed Manchester United.
City, just as we did on Saturday against Sheffield United, got off to a flying start thanks to Jesus.
Burnley keeper Nick Pope could only parry the ball back out and Jesus, following up as all hungry predators do, needed no second invitation to guide a deft header into the gaping goal.
Though Burnley proved obdurate and stubborn opponents in the first half hour, a crucial second goal never seemed far away thanks to City’s fluid, flexible and fabulous football… and it duly arrived on 39 minutes.
Exquisite work from Riyad Mahrez and Ilkay Gundogan opened up the Clarets back line on the right side of the box and a pinpoint cross from the German provided Sterling with the easiest of tap-ins from three yards out.
Mahrez then saw an effort ruled out for offside - albeit by the narrowest of margins - after a VAR check while City had a strong shout for a penalty after Tarkowski tangled with Jesus turned down.
Despite though it was another thorough satisfying night's work for Guardiola and his squad.
A taste for Claret
There’s something about Burnley that brings out the brilliant best in Pep Guardiola’s side.
We have now won our past eight meetings with the Clarets in all competitions by a remarkable aggregate score of 30-1.
This season alone, a 3-0 triumph at Turf Moor in the Carabao Cup in September was then followed by a 5-0 Premier League thumping at the Etihad last November.
Now Guardiola’s side have prevailed again in East Lancashire thanks to another dominant, dynamic display.
Given that record, Sean Dyche and his players will, no doubt, be fervently hoping they do not meet City again in the FA Cup should both sides progress beyond the fifth-round next week!
A 21st clean sheet in all competitions this season also saw equal a club record by recording our sixth consecutive Premier League clean sheet.
Not only are Guardiola's men a potent force going forward, we are emerging as the toughest of nuts to crack at the back.
Another magnificent all-round display by Ilkay Gundogan who was again the centre point of so much of our best work.
The midfielder was again at his mercurial, mesmeric best with his display exemplified by his pin point assist for Sterling's goal.
BURNLEY: Pope, Lowton, Tarkowski, Mee, Pieters, Gudmundsson, Westwood, Cork (Stephens 72), McNeil, Rodriguez, Vydra
Subs: Peacock-Farrell, Bardsley, Long, Nartey, Dunne, Benson, Driscoll-Glennon, Mumbongo
Pep Guardiola's reaction
"We were lucky to score early and after the first half we struggled a bit to break the lines. The second half was much better.
"The start of the second half was the best and in the last 15-20 minutes we just passed the ball with no intention to attack to save energy.
"Everyone knows how tough Burnley is away. In general we are satisfied."
What it means
A ninth straight Premier League success has restored our three-point lead of the top of the Premier League table.
City have 47 points with second-placed Manchester United on 44, with City also having the advantage of a crucial game in hand.
Leicester City are third on 42 while Liverpool lie in fourth ahead of their late kick-off against Brighton later on Wednesday night.
Guardiola’s squad will now begin preparations for Sunday’s eagerly anticipated Premier League trip to Liverpool.
The reigning champions have been showing signs they are returning to their competitive best so the Anfield encounter should be a superb encounter.
Kick-off on Merseyside is at 4.30pm (UK).
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