Ian Goodison returned from suspension to score his fifth goal of the season and Adam McGurk grabbed his first goal for the Club to earn Rovers a 2-1 win at Dean Court.
The Jamaican defender netted from Aaron Cresswell's corner shortly before half time and his effort looked set to give Les Parry's side all three points.
However, when the home side equalised in the dying moments of the game it appeared to deny Rovers what would have been a deserved victory.
But there was still time for McGurk to fire in an unstoppable effort from 18 yards and send the 195 travelling fans home happy.
There were two changes to the side that started at Sheffield Wednesday in midweek with Ian Goodison back from a two match ban and Lucas Akins coming in to the right side of attack. Dropping out of the side were the suspended John Welsh and Dale Jennings who missed out altogether. Andy Robinson returned from injury to be named among the substitutes.
A cagey first few minutes meant neither side created an opening on goal until the seventh minute when Bournemouth's Lauri Dalla Valle had a free header at the far post from Marc Pugh's free kick, but the on loan Fulham striker was ruled offside.
Rovers won a free kick of their own on 11 minutes when Joss Labadie flicked the ball over Shaun Cooper's head only to be brought down by the Cherries defender. However, Aaron Cresswell's effort from a central position 25 yards out went over the bar.
Shwan Jalal comfortably claimed Enoch Showunmi's header from Robbie Weir's cross on 14 minutes and the Bournemouth keeper cut out another Weir cross six minutes later as Tranmere pressed forward at a corner.
Dalla Valle sent an overhead kick high over Tony Warner's cross bar on 21 minutes while Rovers dealt with a couple of Bournemouth corners in quick succession soon after.
After coping with some Bournemouth pressure, Tranmere took the lead on 42 minutes. A corner from Cresswell was whipped in with Ian Goodison reaching the ball first to flick past Jalal from close range. It was the defender's second goal of the season at Dean Court having scored in the 5-3 defeat in the FA Cup earlier in the season.
Akins sent a long range effort wide of the target soon after, the last chance of the half for either side.
Ash Taylor brought a comfortable save out of Jalal four minutes into the second half while at the other end Bournemouth substitute Steve Lovell shot straight at Tony Warner.
Steve Fletcher fired wide of the Tranmere goal on 53 minutes but Rovers were still denying the hosts a decent shooting opportunity with their solid defensive work.
Weir and Taylor missed with efforts for Rovers while Danny Hollands fired wide and a Lovell shot was cleared on its way to goal for Bournemouth as Tranmere maintained their one goal advantage.
Liam Feeney's 20 yard attempt was deflected behind for a corner by Akins, moments before Cresswell was replaced by Adam McGurk.
Max Blanchard came on for the hard working Robbie Weir with a couple of minutes remaining but before he could have any impact on the game, the home side drew level with Danny Ings finding the net from close range on the turn.
But Rovers retook the lead in injury time, with McGurk blasting in his first goal for the Club from the edge of the area, finding the top corner to give Jalal no chance.
Bournemouth: Jalal, Smith (Ings 77), Pearce, Cooper, Cummings, Feeney, Hollands, Robinson, Pugh (McDermott 45 HT), Dalla Valle (Lovell 45 HT), Fletcher. Substitutes not used: Stewart, Purches, Partington, Arter.
Tranmere: Warner, Kay, Goodison, McChrystal, Bakayogo, Weir (Blanchard 88), Taylor, Labadie, Akins, Showunmi, Cresswell (McGurk 80). Substitutes not used: Collister, Wood, Mahon, Fraughan, Robinson.
Referee: Oliver Langford
Yellow cards: Cooper (12), Kay (55), Akins (90+5)
Away attendance: 195
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