A second half free-kick from Ed Upson ensured the Glovers returned to winning ways after Tuesday's defeat at Colchester and condemned the visitors to their sixth defeat in nine league games.
The Somerset side started brightly at Huish Park on Saturday, with Paddy Madden firing into the side-netting before skipper Jamie McAllister's free-kick fizzed narrowly wide.
Rovers hit back when Jean-Louis Akpa Akpro saw his attempt smartly saved by Marek Stech.
After Mamady Sidibe was forced off through injury on the brink of half-time, the hosts came closest to breaking the deadlock - with Madden's low drive brilliantly turned around a post by Owain Fon Williams.
Yeovil took the lead just before the hour mark when Upson deceived the goalkeeper at his near post, curling a 25-yard free-kick into the net to send the Huish Park faithful into raptures.
Upson almost wrapped up the points when his exquisite lob cannoned off the crossbar, with the Glovers surviving a late onslaught to claim a crucial victory.