Torquay produced a spirited performance and the 4-1 final scoreline was very hard on them.
The Merseysiders had luck on their side for their opening goal after five minutes. Eugene Dadi raced through to fire home from an angle for his fourth goal of the season after an error by Jamie Gosling.
United at the time were down to ten men as Brian McGlinchey was off having treatment for a facial injury. He could not return but Matt Hockley proved an able deputy.
The Gulls could not gain a reward for their bright start when Steve Woods and Craig Taylor missed with headers, but they levelled in the 21st minute.
Tony Bedeau raced clear up the right after Tranmere defender Ian Sharps and Michael Jackson collided, and his cross was headed home at the far post by Adebayo Akinfenwa.
Tranmere could easily have regained the lead just before the break but Stuart Boardley cleared off the line from Danny Harrison following a corner.
It needed a fine save by Olafur Gottskalksson to deny Paul Hall early in the second period and Tranmere had to wait until the 66th minute to regain the advantage.
Jason McAteer, who enjoyed a good game in midfield, burst forward from a Gareth Roberts throw in to fire into the left-hand corner from 25 yards.
Hall set up Gary Jones to score Tranmere's third with an excellent finish in the 77th minute.
Hall then put the icing on the cake with an excellent goal of his own in injury time, curling a crisply struck shot from the corner of the box.