Rovers were looking to end a winlees run of two defeats and a draw in their last three games, while visitors Morecambe had won on their last three outings.
The opening minutes saw little goalmouth action, with Rovers top scorer Paul Wanless twice trying his luck from distance, while the home side also had to replace the injured Abdou Sall.
Zema Abbey dragged his shot wide midway through the first half as the home side continued to have the better of things, with the Shrimps failing to trouble Rovers keeper Ryan Clarke.
Conference leading scorer Michael Twiss threatened shortly before the interval, but his shot from the edge of the area was blocked by Jon Richardson and Garry Thompson headed wide in stoppage time.
After the restart Morecambe began to take control of proceedings, but midway through the second period it was Rovers who made the breakthrough.
Bruno Teixeira beat visiting keeper Ryan Robinson from long range after feeding off a pass from Wanless, netting his second goal of the season.
Morecambe boss Jim Harvey immediately made a double change to try and rescue the game, but late efforts from Twiss and Kieron Walmsley were off-target.
Clarke then thwarted Twiss and when Sean O'Connor's header flew wide, Morecambe's last chance had gone.