Billy Kee scored a penalty for Stanley six minutes from time to rescue a point at the Lamex Stadium.
The spot kick was given for handball in the area and, with regular taker Josh Windass substituted, Kee stepped up to send keeper Chris Day the wrong way.
The draw did extend Stanley's record to seven games without a win at Stevenage – but John Coleman would have been happy with a point at the end.
The visitors fell behind in the opening seconds when a Mark Hughes ball into the box found Chris Whelpdale. His initial shot was kept out by Jason Mooney but it fell to Armand Gnanduillet who gave Stevenage a dream start.
The home striker came close to a second soon after but Mooney dived to keep out his effort while Tom Pett rifled an effort wide as Stevenage created the more clear cut early chances.
However Stanley had a great opportunity to get back in it on 19 minutes when Josh Windass raced clean through and tried to chip the ball over Chris Day but the Stevenage keeper did well to deny him.
The Reds had the ball in the back of the net on 25 minutes after Brad Halliday's strike but the assistant's flag was up while a Billy Kee strike was just off-target.
Piero Mingoia was lively on the right wing for Stanley and they did enjoy spells of pressure but Stevenage still looked a threat with a Gnanduillet shot on 35 minutes testing Mooney.The second half was end to end without either team testing the opposition goalkeeper until the 56th minute when goalscorer Gnanduillet broke from the half way line and Mooney had to push out his goalbound effort.
Coleman put on Terry Gornell just after the hour mark as they looked for the all-important goal and Kee wasn't far off with a fierce strike on 67 minutes.
And Day did superbly to deny Seamus Conneely on 72 minutes as his shot sailed through a sea of bodies in the area with the Reds turning up the heat.
Shay McCartan came on as the Reds looked to get back in the game and then Kee stepped up to salvage a point which could be vital in Stanley's promotion push.