Rovers had dispatched Fleetwood Town earlier in the day, but slipped up against a spirited Stanley side.
Ruben Rochina had the first meaningful chance of the game on the quarter hour mark with a low drive that went narrowly wide of the Accrington goal.
Rovers were relieved to see Charlie Barnett's effort go wide of the post after some sloppy play in midfield allowed him a run on goal after half an hour.
Rovers had the first effort after the re-start after substitute Hugo Fernandez was felled on the edge of the area, but David Dunn's strike is well over the bar.
Accrington broke the deadlock shortly before the 70 minute mark and it was a moment Paul Robinson will want to forget. A cross from Adam Rundle was met at the back post by Brian Smikle and his header slipped through the gloves of the Rovers goalkeeper and over the line.
Rovers hit back with an attack of their own as substitute Edinho went close, before Grant Hanley's header was cleared off the line from the resultant corner.
Edinho went closer still with the last kick of the game, but his effort came rocketing back off the post.
Robinson (Usai), Orr (R. Hanley), Hanley, O'Conner, Henley, Lowe, Petrovic, Dunn (Edinho), Rochina, M. Olsson (Fernandez), Goodwillie (Haley).