But non-leaguers Yate, the lowest-ranked side remaining in the competition, were far from disgraced and caused their League Two hosts a number of anxious moments.
The opening goal came after just three minutes when a Tom Warren clearance hit fellow Yate defender Scott Thomas and rebounded into the net.
The Southern League side came back strongly and were denied by the woodwork twice in three minutes, Tom Knigton heading against a post before Jake Cox hit the crossbar with a 25-yard free-kick. But as the first half went on Yate goalkeeper Josh Dempsey was called into action time and time again. He denied Lawson D'Ath and Shaun Harrod midway through the half before palming a 30-yard Russell Penn effort over the bar.
The second half saw Sido Jombati denied by another good save before Cheltenham's pressure finally told when Mohamed headed home a Billy Jones corner after 65 minutes.
Substitute Jeff Goulding put a two-yard effort over and Zebroski hit the visitors' woodwork before then netted a third goal in injury time.