City went into the second leg holding a 2-1 lead over the Cypriot opponents and Mark Hughes' side made a bright start to the second leg, with Micah Richards threatening with an early header.
Fourteen minutes in a fluent City attack ended with Robinho moving away from his marker on the left and flashing the ball across the face of goal and past the far post.
The home side were dominating possession, but were unable to find a breakthrough that would have given them full control of the tie.
Shortly before half-time the impressive Stephen Ireland nearly converted a chance from close range, but his effort was deflected behind for a corner.
Straight after the restart Robinho again threatened from the left side of the area, but again his drilled effort flashed away from the far upright.
However, soon after City took the lead on the night as Robinho again found space down the left and laid the ball back inside for Elano to crash home a low, right-foot shot from 20 yards.
Ten minutes into the second half the Citizens were 2-0 up as a fluent attack ended with Pablo Zabaleta feeding Shaun Wright-Phillips, who took advantage of a lucky rebound to smash a shot past the helpless Antonis Georgallides.
Robinho forced Georgallides into a smart save midway through the second half, before being replaced to a standing ovation around Eastlands.
Omonia got a consolation 12 minutes from time as Rasheed Alabi headed home a right-wing corner at the near post, planting his effort past Joe Hart after shrugging off the challenge of Tal Ben-Haim.
Sub Martin Petrov threatened a couple of times late on, but City had done enough to ensure a safe passage to the group stages.