Ryan Williams and Tim Sills clawed the Shots back into the game in a remarkable second-half turnaround, and in the end Aldershot were unlucky not to end victorious.
Anthony Elding's fifth goal of the season and a Justin Gregory strike five minutes before the break had given Borough a two-goal advantage at half time.
Shots boss Terry Brown made some changes at half time, bringing on Hassan Sulaimani and Nick Crittenden for Tarkan Mustafa and debutant Andre Boucaud. Their energetic infusion and switch to a 4-4-2 formation enabled the home side to draw level through Williams' free kick three minutes after the re-start and a brave header by Sills eight minutes before the end.
Stevenage however will return to Hertfordshire wondering how they were unable to secure all three points given their early dominance and two-goal lead.
Aldershot were only too aware of their defensive vulnerability, having conceded more than two goals per game and Brown mentioned in his programme notes of the need to tighten up at the back.
Stevenage started brightly and wave after wave of Borough attacks tested the suspect Shots rearguard without any real penetration.
That changed on 28 minutes when Elding broke the deadlock. Jon Nurse chased down Barry Laker's free kick with the ball falling to an alert Elding, whose looping header was too good for keeper Nikki Bull.
Stevenage doubled their lead five minutes before the break through a determined Justin Gregory. Mustafa lost possession to Gregory in his own half, and the Borough left-back went past three Shots defenders before blasting past Bull.
With the home crowd roaring on their side, Aldershot halved the deficit with a superb free-kick, which sailed over the Borough wall and Alan Julian into his net.
The Shots, gaining in confidence, went close through Chris McPhee and Williams, but found Julian producing some fine saves. The leveller came through a patient Shots build up, McPhee's cross from the left was met with a ferocious header which Sills dispatched past Julian.