The Glovers were awarded a free-kick on 22 minutes when Godwin Antwi fouled Gavin Tomlin on the edge of the box.
The Rovers' defenders expected a shot but Danny Schofield flipped the ball 20 yards to his left where Yeovil skipper Terry Skiverton was waiting unmarked and hammered a superb drive into the roof of the net.
It was an excellent Yeovil performance after a humiliating five-goal defeat in Tuesday's FA Cup replay at Stockport and they deserved to win by more.
They should have doubled their lead on 47 minutes when Aidan Downes crossed from the right and Tomlin put an eight-yard header straight at goalkeeper Danny Coyne.
Yeovil were hit by injuries and suspensions and were forced to name veteran coach Steve Thompson as a substitute.
It was the same story for Tranmere who had four players out through suspension and injury and were also victims of a flu epidemic.
Ian Moore and Gareth Edds were replaced at half-time and the lively Chris Shuker went off midway through the second half.
But Rovers' goal attempts were few and far between. The best came on 68 minutes when substitute Chris Greenacre brought goalkeeper Josh Wagenaar to his knees.
Yeovil should have added to their lead on several occasions. Downes was robbed by a post at the end of the first half and Skiverton was just off target with a header during a spell of second-half pressure.
Substitute Andy Welsh frittered away a Yeovil chance and the main disappointment for the home team was a booking for the influential Gary Roberts who now faces a suspension.