They were the only clear opportunities Rovers had in a match which saw Yeovil create the better opportunities but lack the finishing touch.
Tranmere had to ride several setbacks. In the 16th minute they lost goalkeeper John Achterberg in a collision with Wayne Gray and, before half-time, right-back Robbie Stockdale had to go off with a pulled calf muscle.
Skipper Ian Goodison played the entire game with an injury - needing lengthy treatment on several occasions - but Rovers stuck to their task and played some neat football in midfield to limit Yeovil to very few opportunities in the first half.
The best came on 22 minutes when a cross-cum-shot from Arron Davies was hooked away and on 38 minutes Leon Best set up an opportunity which just evaded Gray.
The breakthrough came seven minutes into the second half. Tranmere were awarded a throw-in on the halfway line on the right which should have gone to Yeovil. It was taken quickly and Shuker got past Terry Skiverton to fire under the body of goalkeeper Steve Mildenhall from an angle.
It prompted the best period of attacking from Yeovil but substitute goalkeeper Gavin Ward was in excellent form. In quick succession, he saved from Davies, Scott Guyett and Skiverton.
He should have had no chance when Nathan Jones put Best through on 70 minutes but the on-loan striker shot wide.
With Yeovil attacking, Rovers had more space to exploit and when Paul McLaren picked out Shuker the little striker cut in to blast into the roof of the net.
Yeovil knew they were beaten but still pushed forward with Nicky Law - playing his first match on a month loan from Sheffield United - working hard alongside Chris Cohen in midfield.
The final chance came in stoppage time when Best tried his luck from 22 yards but Ward was again up to the task.