Nicky Nicolau's stoppage-time equaliser keeps Hereford's faint chances of snatching the Conference title from their visitors alive.
But realistically, with Stanley leading the table by 16 points and having just nine games to play, this point pretty much clinches the Lancashire side's promotion back to the Football League after 44 years.
Ex-Hereford striker David Brown gave Accrington a first-half lead which was doubled at the start of the second period by Tamika Mkandawire's own goal.
But Stuart Fleetwood followed up to net after Rob Purdie's penalty had been saved and Nicolau popped up in the third added minute to level the scores.
Hereford made the early running and should have gone ahead on eight minutes when Andy Williams made an excellent run down the right before pulling the ball back for Robbie King.
The midfielder had a clean shot at goal but miscued badly as he sent his effort high and wide.
Stanley gradually worked their way into the game but the goal, on 36 minutes, came out of nothing. Andy Todd got the ball to Brown and he hooked it over his shoulder and into the net off a post.
Fourteen minutes into the second period, when Mkandawire sliced Ian Craney's corner into his own net, the game looked well beyond the home side.
But, on 71 minutes, Nicolau's shot from a Ryan Green cross was handled by Daniel Ventre who was immediately red-carded.
Goalkeeper Rob Elliot pushed Purdie's penalty on to the bar, but Fleetwood was quickest to the rebound.
Two more fine saves by Elliot, from Williams and Andy Ferrell, preserved Stanley's lead until three minutes into stoppage time.
Then, Nicolau received Williams' clever flick and drove his first Hereford goal past Elliot to snatch a deserved point for the Bulls.