Paul Dickov wanted his side to get at Bournemouth’s jittery defence right from the outset - but it was the visitors who made the better start at the Keepmoat Stadium.
A Pitman corner from the left whistled across the face of goal, and moments later a short right wing corner found Artur, who was allowed to turn before his goal-bound shot was blocked.
Turnbull just managed to cling onto another dangerous ball into the box with Grabban lurking, before Artur found space 25 yards out and unleashed a well struck shot just wide of the despairing Doncaster goalkeeper’s right hand post.
Fraser then got to the by-line as the Cherries continued to probe but his cross was held by Turnbull.
The lively winger then led a counter attack charge but his effort from the edge of the box was again saved by Turnbull.
Rovers were struggling to settle, and the visitors continued to apply the pressure - this time Daniels’ cross from the left was met by Pitman but his header came back off the bar.
Pitman then tried his luck from a free kick on the edge of the area but it deflected off the Rovers wall and wide.
At the other end Coppinger flicked a Cotterill cross goalwards but it lacked the direction or power to trouble Allsop.
Cotterill then tested Allsop’s handling with a volley from the edge of the area but the goal that had been threatening to come at the other end arrived on the half hour mark.
Daniels’ in-swinging free kick from the right, awarded for a foul by Husband, was glanced into the far corner by PITMAN.
Tensions were running high with the referee as Cotterill was booked for a late tackle on Artur - but Rovers needed to concentrate on their own performance. They had been sloppy in possession and unable to put the visitors under any sustained pressure.
The home side did end the half well though, with a series of corners, but were unable to draw level.
Rovers started the second half like they hoped to begin the first - on the front foot.
But despite some useful approach play they struggled to test Allsop in the Bournemouth goal.
Cotterill and Coppinger swapped flanks, and immediately Coppinger’s left wing centre dropped kindly for Wellens but he could not keep his volley down.
Robinson then tried his luck from distance but the ball again went flying over the bar.
Rovers almost gifted Bournemouth a second when Jones, limping quite heavily, gave possession away cheaply but Ward was not able to capitalise and his 20-yard effort was deflected wide.
Turnbull kept his side in it with a sensational save on the hour mark, at full stretch to his left he palmed away Grabban’s point blank range header from Pitman’s whipped in centre.
Paynter replaced Cotterill midway through the half, hoping to repeat his midweek goalscoring exploits.
Robinson moved out wide but it was not long before he was replaced with Duffy.
Rovers were knocking at the door, without looking overly-threatening in the final third. Coppinger’s volley from the penalty spot hit his own man and went wide to add to the mood of frustration around the Keepmoat.
Duffy was doing his best to add that missing spark. He started the move deep in his own half which ended in Coppinger drilling an effort just wide from the angle of the box.
Grabban’s grass-cutter was easy for Turnbull at the other end, but Bournemouth were refusing to just sit on their lead.
Dickov threw Forrester on for Wabara with 13 minutes left to play, opting to go three at the back and throw caution to the wind.
Grabban headed over substitute Coulibaly’s right wing cross over to keep Rovers interested.
But despite throwing Jones forward in stoppage time there was to be no way through as the Cherries held out for victory fairly comfortably.