Gary Roberts gave Stanley the lead after just four minutes with a rasping drive.
But it wasn't all smiles as the home side slipped 2-1 behind after two goals from Darren Barnard - the second from the penalty spot.
But Aldershot defender Chris Giles received his marching orders for a professional foul in the 61st minute and it didn't take long for Accrington to level matters.
A minute later, Lee McEvilly fired home. However, despite being down to 10 men, Tim Sills restored Aldershot's lead with a clinical finish in the 71st minute.
Accrington, though, were not to beaten and McEvilly bagged his second of the evening in the 78th minute to guarantee a share of the spoils.
Midfielder Ged Brannan was absent for Accrington, serving a one-match suspension following his dismissal at Woking at the weekend, while both Peter Cavanagh and Matty O'Neil remained sidelined through injury.
The home side had opportunities to win in the dying stages but had to settle for a point for their efforts.
Accrington started the better of the two sides and deservedly took the lead. Some good build-up play saw Roberts find space and time before netting with a cool finish.
But credit to Aldershot who, after some dismal results, deserved something from the game.
Barnard finished well on both occasions and for a while it looked like the visitors were going to take all three points.
However, Giles' silly sending off resulted in a frantic finish which could have gone either way.
The Lancashire side can still finish in the top five this season but will have to pick up some points from their remaining matches.