A late goal extended Swindon's unbeaten away run to seven games and they have now lost only once in their last 13 league matches.
They were behind for a long time at Victoria Park, but were always in with a chance against a nervous home team clearly lacking in confidence and their late goal came as no real surprise.
Hartlepool were the better side in the first half and deserved their lead at the break.
Swindon keeper Rhys Evans needed two attempts to save a Michael Maidens volley and pushed a header from Michael Nelson over the bar.
He was also in the right place at the right time to save a header from Anthony Sweeney after a left-wing cross from Richie Humphreys.
He was beaten on 36 minutes when Gavin Strachan, back in the starting line-up after a spell out of favour, struck his low 25-yard free-kick through a gap in the wall and it sneaked into the bottom corner.
Home keeper Dimi Konstantopoulos earlier did well to keep out a shot from Aaron Brown and even better to push a header from Charlie Comyn-Platt around his left-hand post.
Nelson had a header cleared off the line early in the second half and Konstantopoulos did well to push a curling free-kick from Comyn-Platt around his left-hand post when the 25-yard shot looked a certain goal.
But the goal arrived on 78 minutes when Ricky Shakes ran well on the right before crossing to the near post for Rory Fallon to score his 13th goal of the season with a great diving header.
Hartlepool battled in an attempt rescue the three points but Swindon held on without too many problems and were full value for the point as their recovery from an awful start to the season continues.