Despite a late reply from Danny Woodards, the home side are now in the thick of the battle to avoid the dreaded drop after a desperately poor display.
Coulthirst headed Torquay in front in the 62nd minute from a Courtney Cameron free-kick and 13 minutes later the on-loan Tottenham striker turned goal-maker, teeing up Mansell to fire past Steve Mildenhall with the aid of a deflection from 12 yards.
The game was deep into stoppage time when Woodards shot home at the second attempt after Torquay goalkeeper Martin Rice had saved his first effort.
A tense first half saw both sides struggle to create chances. Torquay striker Elliot Benyon forced a save from Steve Mildenhall with a smart turn and volley just before the break.
Chris Beardsley headed over when he should have hit the target in the opening exchanges, but the best Rovers could manage was a long range shot from Michael Smith that cleared the crossbar.