The Premier League leaders extended their club-record winning run to 13 matches across all competitions, with the result rarely appearing in doubt from the moment Jesus capitalised upon a third-minute error by Nick Pope.
Sterling claimed his 10th of the season seven minutes before the interval, after which point City’s football continued to flow but the goals dried up.
Pep Guardiola’s side are three points clear at the summit with a game in hand on Manchester United, with champions Liverpool next on their agenda this weekend.
RESULTS | POINTS TABLE | FIXTURES
Sterling darted inside from the left to play in Bernardo Silva, whose shot was poorly dealt with by Pope to leave Jesus with a simple leaded finish.
Pope looked to be in trouble again when he charged out of his area to confront Sterling in the 20th minute but the England goalkeeper managed to get a timely foot in.
City had to bide their time as Burnley grew into the contest but a wonderful link-up between Riyad Mahrez and Ilkay Gundogan allowed the latter to drill across goal for Sterling to convert from close range.
Joao Cancelo fired too close to Pope just before half-time and Burnley’s number one sharply thwarted Sterling early in the second period as the visitors looked to conclusively end the argument.
Mahrez thought he had but was fractionally offside when he steered in Jesus’ cross.
Burnley finally registered a shot in the 64th minute when Matej Vydra acrobatically volleyed over, but waves of slick City attacks continued to arrive.
Ederson decided to involve himself in the action by clattering through Erik Pieters and provide the strange spectacle of a goalkeeper getting booked for a foul on a left-back.
It was the closest City came to a scare.
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