Rovers lost Dean Saunders to Wolves on Monday and it looked like it would coincide with Rovers' first defeat in five when James Dunne struck for Stevenage in the 66th minute.
However, the South Yorkshire side equalised 13 minutes later when Iain Hume pounced after Dave Syers' shot was blocked by Steve Arnold before Jones headed home the winner in stoppage time and Rovers made it a club-record 12 away games without defeat.
Stevenage striker Marcus Haber had the first sight of goal but nodded Greg Tansey's corner back across the six-yard box while at the other end Hume tested Arnold.
Boro snatched the initiative in the 66th minute when Tansey's corner was cleared as far as Dunne, who smashed a stunning right-footed volley into the top corner.
However Rovers restored parity with 79 minutes played as Syers saw his effort repelled by Arnold before Hume slammed home the rebound.
And the visitors then won it in the fourth minute of stoppage time as Jones rose highest to convert David Cotterill's left-wing corner.