Darrell Clarke's side travelled to Shropshire having won just once in five Conference Premier encounters, but the away following were encouraged after Jake Gosling capitalised on a misplaced back pass before directing his strike wide of the mark.
Ellis Harrison and Ollie Clarke also tried their luck from distance as Telford, despite competing well in the middle of the pitch, struggled to mount any kind of a threat on the visitors' goal.
Chances continued to be few and far between, with Tom Parkes trying to offer some magic from long range, but his 40-yard attempt was never going to trouble goalkeeper Freddy Hall.
Lee Mansell was provided with an opening for Rovers shortly after the half-hour mark, but he could only miscue his shot wide after good work from Andy Monkhouse.
The away outfit had a late chance to open the scoring, but Gosling's set piece evaded everyone at the back post before going behind for a goal kick.