Colchester started well and it needed a sharp save by goalkeeper Tony Warner to deny Anthony Wordsworth after just two minutes.
At the other end Ian Goodison and Lucas Akins got in weak attempts which posed no real danger for Ben Williams and Showunmi missed the target after good approach work.
Andy Robinson fired just over as Tranmere pressed soon after the break and it was his pass in the 53rd minute which set Showunmi clear to put an angled shot past Williams.
The visitors showed more sparkle but Steven Gillespie wasted a good headed opportunity on the hour. Then substitute Andrew Bond saw an effort headed off the line by Aaron Cresswell.