Manchester City s Nathan Ake, centre, celebrates with Manchester City s Jack Grealish, left, after scoring his side s second goal during the English Premier League soccer match between Leeds United and Manchester City at Elland Road in Leeds, England, Saturday, April 30, 2022. AP
Rodri and Nathan Ake got the vital goals from set pieces on a day City needed to match the aggression of the home side before Gabriel Jesus and Fernandinho sealed victory late on.
Pep Guardiola's men edge one point ahead of the Reds once more with four games remaining for both sides.
The defeat leaves Leeds looking over their shoulder at the relegation zone.
Burnley's dramatic come-from-behind win at Watford earlier on Saturday pushed Jesse Marsch's men down to 17th.
They still enjoy a five-point lead over Everton, but the Toffees have two games in hand to haul themselves out of trouble.
Leeds also appear to have the tougher run-in with Arsenal and Chelsea among their final four matches.
Guardiola clearly had one eye on Wednesday's Champions League trip to Real Madrid as he made five changes from the side that beat the newly-crowned Spanish champions 4-3 in a thrilling semi-final, first leg on Tuesday.
Kevin De Bruyne, Bernardo Silva and Riyad Mahrez were among those left on the bench.
Joao Cancelo also returned to the back four after being suspended in midweek, but the Portuguese nearly gifted Leeds the lead inside five minutes.
Cancelo's slip on the halfway line allowed Rodrigo to burst clear, but the Spanish international should have picked out the unmarked Raphinha rather than going for goal himself as his shot was easily blocked.
Leeds were flying into tackles like a side battling for survival, but that aggression was their downfall for the opening goal.
Raheem Sterling was upended on the left wing and from the resulting free-kick Rodri headed home Phil Foden's inviting free-kick.
Guardiola can ill afford more defensive injuries with Kyle Walker possibly ruled out for the season and John Stones struggling with a muscle problem.
Aymeric Laporte was involved in a sickening clash of heads with Robin Koch, but both players were controversially allowed to continue after receiving lengthy treatment.
Ake also went off in the second half, but by that point the Dutchman had made arguably his most telling contribution in nearly two seasons as a City player.
Ruben Dias headed Foden's corner across goal and Ake turned home from close range to spark wild celebrations on the City bench.
Jesus then maintained his scoring streak by latching onto Foden's pass to smash home his sixth goal in his last three games.
Fernandinho completed the rout and took City's goal difference to within one of Liverpool's with a sweet strike in stoppage time.
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