Rovers got off to a bright start and deservedly took the lead in the 17th minute when Craig Disley set off on a long run from the right and fired a good low shot past Chris Weale from the edge of the box.
Yeovil's reply was an equally good goal in the 26th minute when Phil Jevons picked up the ball from a throw-in and smashed it into the roof of the net from 25 yards.
Yeovil were now taking up the running against a Rovers team weakened by injuries and both Jevons and Gall went close to giving them the lead.
Yeovil started the second half in style and might have taken the lead in the 46th minute when Arron Davies, preferred to Latvian international Andrejs Stolcers, got to the far post to connect with a cross but the ball ran along the goal line and was cleared.
In the 52nd minute, however, Yeovil did take the lead. In a scramble following a corner, Rovers' central defender Christian Edwards handled on the ground and Jevons stroked in the penalty.
On 63 minutes, the former Everton and Grimsby striker completed a hat-trick when he headed in Andy Lindegaard's right wing cross from practically under the cross bar.
Cheered on by a crowd of 9,153, the largest attendance since they joined the Football League, Yeovil powered forward and made it 4-1 with another excellent header from the hard-working Bartosz Tarachulski.
Yeovil eased up in the final 10 minutes but it was not until the 85th minute that Rovers managed their first shot of the half, and two minutes later they scrambled in their second goal, Richard Walker the marksman from close range.