After being held to a 2-2 draw by Newcastle United on Saturday, Pep Guardiola’s team desperately needed to beat the Clarets to give their fading title challenge a boost and they clinched the three points in style thanks to a fine display.
After Jesus had seen a back-heeled effort rightly ruled out for offside, the Brazilian broke the deadlock in the 24th minute with a sublime curling effort that was too good for Burnley goalkeeper Nick Pope.
Raheem Sterling went close to doubling City’s lead when he latched on to Kevin de Bruyne’s cross but Pope saved the England man’s effort with his knee.
When Sean Dyche’s team created a rare opening, Dwight McNeil’s shot was blocked but City always looked dangerous whenever they moved forward and they doubled their advantage five minutes after the interval when Jesus lashed a volley home from Bernardo Silva’s cross.
Jesus went close to completing his hat-trick when he bent a shot inches wide before Rodri made it 3-0 in the 68th minute, lashing a rising 20-yard shot into the roof of the net.
City strolled through the rest of the match and Riyad Mahrez fired a low 87th-minute shot home before Robbie Brady grabbed a consolation goal for the Clarets.
Guardiola’s team can now start thinking about the Manchester derby on Saturday while Burnley travel to London to play Tottenham.