At the other end, Rovers forward Gary Jones should have done better with a free header.
They then lost their number 1, John Achterberg, in the 21st minute after he came out worse in a challenge with Delroy Facey. Substitute 'keeper Russell Howarth came off the bench to replace him.
Stuart Elliott was denied a penalty when the referee adjudged ex-Tiger Ian Goodison took the ball in a tackle.
Boaz Myhill had to make a top drawer save to keep out Jones and clear the danger.
City took a surprise lead in the 34th minute through captain Ian Ashbee. He hit a long-range shot with his left foot, which took a deflection as it flew into Howarth's bottom corner for his first goal of the season.
Elliott almost got to a Ryan France through ball, but Howarth was able to snatch it from his feet. He hurt himself in doing so though, and play eventually resumed after a bandage was applied to his head. Elliott was booked for the challenge.
The temperature of the match was rising, with Jones and Stuart Green going into the book, and the referee was booed off at half time.
Tranmere came out after half time without Howarth who was still suffering from the injury he suffered in the first half, so bizarrely ex-City midfielder Theodore Whitmore came on as substitute to take over in goal.
The Jamaican was beaten 9 minutes into the half by Elliott. France crossed, Facey flicked it on, and Elliott got another deft header on it to put it past Whitmore.
But the visitors hit back through Eugene Dadi a minute later, who had come on as a sub earlier in the half. He turned well before squeezing in a great shot which zipped into the bottom corner of Myhill's goal.
Straight from the restart, City restored their two-goal advantage though. Facey crossed and Nick Barmby ran the ball in.
Myhill made another great save to keep out Roberts's free kick, before City struck again in the 68th minute. Substitute Danny Allsopp played the ball on, and Elliott raced through to smash the ball into the top corner.
5 minutes later, Elliott got his third goal - his first hat-trick for the club. A spell of passing led to the Northern Irishman running onto Barmby's ball into the box, before being taken down by Jackson. Regular taker Green allowed Elliott to take the penalty, which he blasted low into the middle of the goal. However, the referee ordered it to be retaken because of players entering the penalty box. Elliott again netted, putting it to Whitmore's right this time, making it 19 goals in all competitions for him this season.
The scoring was completed by Allsopp in the 89th minute to finish it at 6-1. Green's corner was headed on by Damien Delaney, and the Australian knocked it in from close range.
Although there was little Whitmore could do about any of the goals he conceded, the goalkeeping situation clearly affected Brian Little's side's performance as they were crushed by their promotion rivals in front of 20,064 people.
City line-up (4-4-2): Myhill; Joseph, Cort, Delaney, Edge; France, Green, Ashbee, Elliott (Keane 75); Facey (Allsopp 64), Barmby (Wilbraham 77).
Un-used subs: Duke, Lewis.