Rovers keeper Steve Phillips made a string of great second-half saves, two in particular from Matty Robson keeping his side in the game.
Hartlepool took the lead on six minutes, Michael Nelson heading in from six yards after Robson's high cross from the right, when his corner was returned to him by Kevin Kyle.
But Rovers posted a warning on 23 minutes when the lively Jo Kuffour's low shot from a couple of yards outside the area was well saved by Arran Lee-Barrett as the keeper dived low to his left.
And on 25 minutes the threat turned into a goal when Joe Jacobson's pass into the area caught out the home defence and Jeff Hughes went wide on the left as he rounded Lee-Barrett before scoring with a low angled shot.
Kyle blasted a terrific shot from the right of the area just over the Rovers bar on 28 minutes, but on 34 minutes Rovers should have gone in front.
Aaron Lescott crossed low from the left and when Kuffour dummied at the near post, Craig Disley was presented with a great chance eight yards from an open goal, only to blast his shot wide.
After the break it was all Hartlepool and after Kyle had shaved the top of the bar with a header from a Robson corner, Robson twice brought the best out of Phillips, both with angled shots from wide on the left of the area.
Joel Porter also blasted a cross from the left against the post as the home team dominated the end of the game, but they couldn't find a way through.