A Billy Kee brace and Seamus Conneely's late penalty consigned the hosts to another season in the English Football League's bottom tier.
Stevenage top scorer Matt Godden sent an effort into the side netting on two minutes, while Stanley almost took the lead shortly after when Conneely had a shot cleared off the line.
Connor Ogilvie was denied by Marek Rodak between the Stanley posts, before Jamie Jones saved from Sean McConville at the other end as both sides pressed.
With 20 minutes to go, Accrington took the lead from the spot. Kee converted after Seamus McCartan was felled in the area.
Rodak tipped away a Godden header that was destined for the top corner as the home side rallied.
But Accrington added a second when McCartan squared for Kee to bury his 15th goal in all competitions this season.
And the away supporters were jubilant when their team notched a third as Conneely converted a second spot kick.
Match report supplied by the Press Association.
Match ends, Stevenage 0, Accrington Stanley 3.
Second Half ends, Stevenage 0, Accrington Stanley 3.
Goal!  Stevenage 0, Accrington Stanley 3. Seamus Conneely (Accrington Stanley) converts the penalty with a right footed shot to the high centre of the goal.
Penalty conceded by Luke Wilkinson (Stevenage) after a foul in the penalty area.
Penalty Accrington Stanley. Seamus Conneely draws a foul in the penalty area.
Hand ball by Tom Pett (Stevenage).
Attempt saved. Luke Wilkinson (Stevenage) right footed shot from outside the box is saved in the top centre of the goal.
Attempt missed. Terry Gornell (Accrington Stanley) right footed shot from the left side of the box misses to the left.
Corner,  Accrington Stanley. Conceded by Luke Wilkinson.
Attempt blocked. Sean McConville (Accrington Stanley) right footed shot from the right side of the box is blocked.
Substitution, Accrington Stanley. Terry Gornell replaces Billy Kee because of an injury.
Foul by Luke Wilkinson (Stevenage).
Billy Kee (Accrington Stanley) wins a free kick in the attacking half.
Sean McConville (Accrington Stanley) is shown the yellow card for a bad foul.
Tom Pett (Stevenage) wins a free kick in the defensive half.
Foul by Sean McConville (Accrington Stanley).
Goal!  Stevenage 0, Accrington Stanley 2. Billy Kee (Accrington Stanley) right footed shot from the centre of the box to the bottom left corner. Assisted by Shay McCartan.
Attempt saved. Matt Godden (Stevenage) header from the centre of the box is saved in the centre of the goal.
Corner,  Stevenage. Conceded by Matty Pearson.
Foul by Jobi McAnuff (Stevenage).
Billy Kee (Accrington Stanley) wins a free kick in the defensive half.
Substitution, Stevenage. Jamie Gray replaces Dean Wells.
Goal!  Stevenage 0, Accrington Stanley 1. Billy Kee (Accrington Stanley) converts the penalty with a right footed shot to the centre of the goal.
Penalty conceded by Charlie Lee (Stevenage) after a foul in the penalty area.
Penalty Accrington Stanley. Shay McCartan draws a foul in the penalty area.
Foul by Charlie Lee (Stevenage).
Scott Brown (Accrington Stanley) wins a free kick in the attacking half.
Corner,  Accrington Stanley. Conceded by Luke Wilkinson.
Attempt missed. Jordan Clark (Accrington Stanley) right footed shot from the centre of the box is just a bit too high.
Jobi McAnuff (Stevenage) is shown the yellow card for a bad foul.
Foul by Jobi McAnuff (Stevenage).
Matty Pearson (Accrington Stanley) wins a free kick in the defensive half.
Attempt missed. Steven Schumacher (Stevenage) right footed shot from the centre of the box is too high.
Matty Pearson (Accrington Stanley) is shown the yellow card for a bad foul.
Jobi McAnuff (Stevenage) wins a free kick in the defensive half.
Foul by Matty Pearson (Accrington Stanley).
Tom Pett (Stevenage) wins a free kick in the attacking half.
Foul by Scott Brown (Accrington Stanley).
Foul by Matt Godden (Stevenage).
Janoi Donacien (Accrington Stanley) wins a free kick in the defensive half.

Sum: Stevenage missed out on a place in the League Two play-offs after losing 3-0 at home to Accrington.


Kyle Coetzer hit 127 and captain Preston Mommsen 111 not out as the Scots made 327-5 after being put in.
Coetzer, Mommsen and Richie Berrington (27) all passed passed 1,000 ODI runs - joining two other Scots, Neil McCallum and Gavin Hamilton - in the process.
The Scots then bowled out the visitors for 229, with Alasdair Evans taking 4-41 in the Edinburgh sunshine.
"We always wanted to bat first and put some runs on the board," said skipper Mommsen.
"We built a very good platform through Craig Wallace and Kyle Coetzer up top. That gave us a base to really kick on through the middle and towards the back end of the innings. Everyone who came in contributed."
Coetzer, who scored his first century on Scottish soil, stressed the importance of getting a win after a disappointing defeat by Afghanistan in July.
"We put in decent performances [against Afghanistan] but we lost our way at crucial moments in the game. Fortunately for us today we managed to piece that back together and get it right."
Victory helped sooth Scotland's frustration at their rain-affected ICC Intercontinental Cup fixture with the UAE at Ayr earlier in the week, when only 59 overs were possible over the four days.
"The guys were pulling their hair out," Coetzer added. "We just wanted to get on it with and so we were raring to go today."
The teams meet again at the Grange on Tuesday in the second one-dayer.

Sum:
Scotland beat United Arab Emirates by 98 runs in their World Cricket League Championship one-dayer at the Grange.