But it was no more than the Cherries deserved after they had dominated for long periods earlier in the game without being able to find a pay-off punch.
Doncaster struggled at the start and they were fortunate to escape in the fifth minute when Steven Foley-Sheridan hammered a volley against the crossbar after latching on to a throughball from Callum Hart.
Visiting keeper Gareth Stewart did well to parry a spectacular 20-yard volley from Sean Thornton three minutes later but the home side saw little of the ball for some time after that.
Bournemouth established a stranglehold in midfield and dominated possession to pin the home side back deep into their own half.
Rovers boss Dave Penney made some positional changes in midfield to combat the visitors style of play and it seemed to work as Rovers began to edge their way into the game.
James Coppinger was unfortunate when he beat Stewart with a fierce angled drive in the 35th minute only to see hard-working defender Karl Broadhurst clear off the line.
Big striker Mark McCammon headed wide from Thornton's right-wing cross and then Lewis Guy wasted a chance when he needed one touch too many in a crowded penalty box just before the interval.
Doncaster stepped up the pace in the second half with Guy firing across the face of goal before McCammon had a header saved in the 54th minute.
They finally made the breakthrough six minutes later when Gareth Roberts and Steve Roberts combined to create a simple chance for Guy to tap the ball home from close range at the far post.
On-loan striker Leon Best had a header saved when Bournemouth tried to hit back in the 63rd minute before Coppinger was denied by another Broadhurst goal-line clearance a minute later.
Rovers seemed to be heading for victory but Steve Roberts was penalised for a blatant handball offence in stoppage time and Hayter stepped up to coolly send Alan Blayney the wrong way, slotting the spot-kick inside the keeper's right-hand post.