It still looks like mission impossible for Pools but Austin's goal after 10 minutes ensured their fate is still not sealed.
Hartlepool's Jonathan Franks and Tranmere's Jean-Louis Akpa Akpro both saw chances narrowly miss the target in a lively opening spell.
But Rovers temperatures were raised when referee Lee Collins pointed to the penalty spot after ruling that Ben Gibson had held Sam Collins in the box.
The hosts thought justice had been served when Owain Fon Williams saved Simon Walton's spot-kick but Austin pounced to slide home the rebound.
Andy Robinson almost produced a 37th-minute equaliser when he tricked his way beyond two Hartlepool defenders before seeing his shot strike the outside of a post.
And he suffered a similar agonising fate when Rovers were awarded a penalty of their own 12 minutes after the break, with Scott Flinders superbly tipping his effort onto the crossbar after Peter Hartley was judged to have felled Akpa Akpro.
Tranmere substitute Cole Stockton flashed a 73rd-minute shot over the bar shortly after entering the action.
But that was to be as close as Rovers came to rescuing anything from the game, with Akpa Akpro's wildly-struck free-kick just about summing up Tranmere's day late on amid a chorus of boos at the final whistle.