The hosts edged ahead when Craig Dawson met Nicky Adams' freekick in the 72nd minute to head home.
Their advantage appeared to be boosted when Dave Penney's side were reduced to 10 men, Cian Bolger dismissed soon after Dawson's effort for his second bookable offence.
But Will Hoskins demonstrated exactly why he is attracting interest from Championship clubs when he gathered Rene Howe's pass and fired wide of Owain Fon Williams in the Dale goal.
The 10 men looked on course for a point until Akpa Akpro fired home from a tight angle and their disappointment was compounded when Chris O'Grady released Matt Done and he rounded Luke Daniels before slipping the ball into an empty net.
Owain Fon Williams had earlier kept out Rene Howe's drive with a fine instinctive save while Hoskins had fired over after turning sharply in the area.
Rochdale 3-1 Bristol Rovers: Match Report - view commentary, squad, and statictics of the game as it happened.