Gavin Tomlin was fouled on the edge of the box in the League One clash at Huish Park and while Rovers' defenders were expecting a shot, Danny Schofield switched the ball 20 yards to his left where skipper Terry Skiverton hammered in a terrific right-footed drive from outside the box on 23 minutes.
It was no more than Yeovil deserved for a spirited performance, and they could have added further goals but once again struggled to provide the killer blow.
They should have made it two when Aidan Downes picked out Tomlin with a right-wing cross but the young striker, eight yards out, headed straight into the arms of keeper Danny Coyne.
Rovers' attempts were few and far between but substitute Chris Greenacre brought a good save from home keeper Josh Wagenaar in the 68th minute.
The result moves Yeovil up to 19th place, while Rovers are in 11th position.