Rovers had to wait until the 80th minute to claim three precious points but it was no more than they deserved for a dominant display.
Swindon were forced back for most of the match and home goalkeeper Gary Woods never had a single shot to save.
There was little goalmouth action in the first half as both sides packed the midfield, but Swindon were fortunate to survive appeals for a penalty when Aden Flint appeared to bring down Dean Furman in the 29th minute.
Rovers stepped up the pace in the second half and Town keeper Wes Foderingham did well to save a swerving effort from Kyle Bennett following neat interplay between Furman and James Coppinger.
McCombe had a header tipped away by Foderingham in the 66th minute and Andy Griffin volleyed just wide from the resulting corner.
Flint was fortunate again when he appeared to push Chris Brown in the penalty area in the 68th minute but Rovers' pressure finally paid off 10 minutes from time when McCombe headed home from David Cotterill's corner.