Pep Guardiola’s side had to respond after Liverpool beat Newcastle and they did just that, with Rodri heading them in front early on. Leeds made it uncomfortable though and threatened to make City stumble in the race.
But Nathan Ake doubled the lead after the break and Gabriel Jesus put the result beyond doubt, before Fernandinho capped the win with the final kick of the match to maintain City’s one-point advantage with four league matches remaining.
Their focus now turns to the Champions League, as they travel to the Bernabeu to face Real Madrid on Wednesday.
As Liverpool did earlier in the day, Guardiola shuffled his pack with Bernardo Silva and Kevin De Bruyne among those named on the bench.
Leeds had a big chance to take a shock early lead, when a City corner was cleared out to the halfway line. Joao Cancelo was the last man and he slipped, allowing Rodrigo to charge clear for the home side. He should really have squared it to Raphinha, but took too long to make his decision and the space disappeared.
With 13 minutes on the clock, City scored the opening goal themselves. It was incredibly simple too – Phil Foden swung in a brilliant free-kick delivery and Rodri had space in the box to head into the far corner.
A nasty clash of heads between Robin Koch and Aymeric Laporte stopped the match and when it resumed, Leeds had their best spell. They rushed City and created some promising moments, but could not turn those into clear-cut chances.
Gabriel Jesus fired straight at the goalkeeper after working space in the box, before Stuart Dallas was forced off with what looked to be a serious injury. The Leeds man clattered into Jack Grealish and in doing so was stretchered off himself.
City took complete control of the match after the break and it came through another set-piece. The corner was swung in deep, Ruben Dias won the initial header and it fell to Ake who swept home the finish from close-range.
Jesse Marsch moved Jack Harrison and Raphinha to wing-back as he threw everything he could at City in the final 25 minutes at Elland Road, but that left them exposed at times. Raheem Sterling had plenty of joy down the right, while Ilkay Gundogan sent a shot from distance wide before he had another from inside the box blocked.
Raphinha went close to halving the deficit and setting up a grandstand finish, with Laporte sliding in brilliantly to deflect the Brazilian’s shot over the bar.
Any hopes of a Leeds comeback were ended for good by Jesus with just over ten minutes remaining, finishing emphatically after Foden played him in with a wonderful pass.
Cancelo could, and probably should, have added a fourth late on when clean through, before Fernandinho did just that deep into stoppage-time when he rifled it low into the far corner from the edge of the box.