Accrington came into the game on the back of a 13-match unbeaten run which stretched back to mid-March, but they never reached their best form and were comfortably dealt with by Graham Westley's disciplined side.
Stacy Long opened the scoring with a deflected effort from the edge of the box before Joel Byrom profited from poor defending to prod in the second.
Stevenage are now favourites to book a place at Old Trafford but John Coleman's side have only lost three times at home all season and could be a different proposition on their weathered Crown Ground pitch.
Westley's side beat Newcastle in the FA Cup earlier this season and could cap a remarkable first year in the Football League with promotion.
Stanley winger Jimmy Ryan has been linked with an improbable summer move to Spanish side Real Zaragoza in recent weeks and had the first effort but his stinging volley was well blocked by Ronnie Henry.
Long then had the first sighter for the hosts, cutting in from the left to send a curling effort just wide of Alex Cisak's far post.
Stevenage captain Mark Roberts hooked an effort over from a corner before the home side took the lead in the 24th minute.
Henry's throw-in was held up well by striker Craig Reid and laid back to the edge of the area for Long to drive in a shot which was deflected past the dive of Cisak.
Darius Charles came close to a spectacular second when his volley from fully 25 yards looped over Cisak but came back off the inside of the post.
Stevenage were well on top and doubled their lead just before the break through Byrom.
Henry crossed from the right, Charles won the knock-down and midfielder Byrom was brave to get to the bouncing ball before a hesitant Cisak and loop a shot into the vacant net.
Stanley knew they had to breach the best defence in the division to claw their way back into contention after the break but, despite the superb support of their travelling fans, they struggled to make an impression.
Ryan and Terry Gornell combined well to get in behind on a rare attack but Stevenage easily cleared while Long threatened at the other end with a long-range hit which was held by Cisak.
Stanley's Sean McConville was then played in on goal by an errant backpass from Scott Laird but the winger hesitated as he tried to round Chris Day in the Stevenage goal and Ryan eventually fluffed the chance into the side-netting.
It was a dreadful miss and the visitors were then lucky not to be reduced to 10 men after Luke Joyce cynically scythed down Long as Stevenage mounted a three on one counter-attack.
Joyce escaped with a booking as both sides struggled to create much in the closing stages and Stevenage closed out the win.