The Gulls, who had not won since Boxing Day, tore Rovers apart early on and were 2-0 up in 19 minutes.
After only seven minutes an end-to-end six-man move ended with Tony Bedeau crossing for Leon Constantine to head home.
Then Rovers' defence failed to deal with a long ball by Steve Woods and former Doncaster striker Bayo Akinfenwa had room and time to spare to nod the second over Andy Warrington.
It was the second goal Akinfenwa had scored against his old club this season. On-loan goalkeeper Phil Barnes from Sheffield United had only one save to make in the first half of a faultless debut.
But it was a different story in the second half.
Galvanised by a half-time roasting from manager Dave Penney, Rovers hammered away, hitting the post through Michael McIndoe and seeing Barnes make a great full-length save from Greg Blundell.
Tempers flared midway through the second half, with referee Trevor Parkes booking four players – Torquay's Tony Bedeau and Rovers' Paul Green, Tim Ryan and McIndoe – after a 63rd minute fracas.
Substitute Simon Johnson, on loan from Leeds, finally pulled a goal back with his first touch in the 87th minute, tapping home from close range after a brilliant run and cross by McIndoe.
But it was too little and too late for Rovers.