Michael Higdon scored what proved to be the decisive goal, heading home Lee Vaughan's cross just before the hour.
Torquay almost grabbed a late equaliser when Luke Young's 25-yard free-kick was saved by Scott Davies, but Rovers held onto the lead to move three points clear in the final play-off position.
The Gulls remain in 18th with a three-point cushion from the division's relegation places.
Tranmere consolidated their play-off position with a narrow win at Torquay.