Arch-rivals Sheffield Wednesday had climbed above the Blades in the table earlier thanks to a 2-1 victory at Brentford.
Goals from Joel Byrom and Scott Laird put the visitors in command before Richard Cresswell and Matt Lowton scored to set up a tense finish.
The hosts threatened inside the first minute when Michael O'Halloran and Chris Porter both failed to make the most of a searching cross from Stephen Quinn.
A Luke Freeman shot was deflected wide before Byrom opened the scoring in the 31st minute, guiding the ball past Steve Simonsen after meeting Patrick Agyemang's low cross.
Laird put Stevenage further ahead, two minutes after the restart, drilling a low shot past Simonsen from about 20 yards out. Substitute Cresswell's 63rd-minute header gave United hope and Matt Lowton equalised in the 85th minute after Harry Maguire's ball into the area was headed down into his path.