After picking up just the one point from games with Arsenal and Chelsea, it was imperative that City got back on track on Saturday afternoon and the signs were good from the early stages as David Silva and Leroy Sane both went close, eventually being denied by Eldin Jakupovic.
Hull were showing a threat on the break but they were not creating any clear-cut openings, and it was City who dominated throughout the remainder of the first half.
Aguero dragged a shot wide when he should have done better, before Delph sent two efforts off target in the space of three minutes.
Yaya Toure then hit a shot over the crossbar, before he went close twice in quick succession with Jakupovic tipping his free kick over before the Ivorian sent a header off target.
However, City finally took the lead after 31 minutes when Elmohamady turned the ball into his own net after a good cross from Jesus Navas.
Moments after the goal, Silva diverted an attempt over the crossbar after meeting a cross from Raheem Sterling, but Kamil Grosicki offered a bit of encouragement for the visitors when shooting wide from distance.
Hull needed to return for the restart with the intention of not allowing City to double their lead, but they did just that with three minutes gone in the second half.
A terrific team move ended with Sterling providing the cross for Aguero, and he made no mistake with the finish from inside the penalty area.
Silva wasted little time before starting to make changes to his team, but the game was effectively over as a contest once Delph scored a third for City.
Sterling was again the provider, this time teeing up his teammate on the edge of the area, and the midfielder did the rest with a fine finish into the net for his fifth goal in a City shirt.
City were able to go through the motions with Pep Guardiola making full use of his substitutions but with five minutes left, it was a Hull replacement who helped the Tigers pull one back.
City avoided any further scares, however, and they now sit seven points clear of Arsenal, although the Gunners do have two games in hand.