But if the Pep Guardiola's boys had thought the encounter was going to be another routine victory on the road, they were jolted to reality in the 82nd minute, when Johann Berg Gudmundsson latched on a cross by Mathew Lowton to even scores for the hosts.
City were leading through Danilo's 22nd-minute strike but missed a number of chances to finish off the game with Sterling being the worst of them, when he failed to find the target from two yards.
And for nobody more so than Sterling.
That advantage was 16 points by the full-time whistle at Turf Moor, and City is just eight wins away from securing a third title, although it was reminded of the league's many hazards by Sean Dyche's obdurate outfit.
With City dominating the game at 1-0 but looking for that killer second goal, Sterling was set up for what looked like a formality halfway through the second half.
"The next day you focus on the next one (chance)".
"Of course we are frustrated in terms of the result but the performance was outstanding against a Burnley side who are the most British of teams in terms of long balls and the way they play", said Guardiola after the Premier League game.
But somehow he missed a chanced which looked easier to score.
"What they have done this season, Burnley, is unbelievable".
"Of course we are sad for the dropped two points, but to come here and play the way we played is nearly impossible", he said".
"We played so good", Guardiola told Sky Sports. "They are injured. I would like to have 18 players, but we had 17". Sterling somehow put the ball wide just one metre out from the empty goal.