Bournemouth extended their unbeaten League run to seven matches thanks to a second-half equaliser from leading scorer Warren Feeney.
Tranmere enjoyed the better of the opening period and Gareth Roberts saw an excellent 18th minute effort turned onto a post by keeper Neil Moss.
Feeney missed a great chance for the Cherries three minutes later when he had only goalkeeper John Achterberg to beat but put his shot wide of the right hand post.
Rovers got the breakthrough after 32 minutes when skipper Graham Allen prodded the ball home after Eugene Dadi headed down a Roberts corner.
Two minutes later Iain Hume went close to doubling the margin but flashed his shot just over from 20 yards.
Bournemouth looked a much-improved side in the second half.
James Hayter fired wide from 20 yards, but in the 72nd minute provided the perfect throughball for Feeney to lob Achterberg for the equaliser.
Sixty seconds later the Bournemouth striker brought a terrific save from Achterberg, before Wade Elliott and Stephen Purches put good efforts over as the game finished level.
Bournemouth boss Sean O'Driscoll said: "We had our poorest first half for a long time but we were tremendous after the break.
"We made a real game of it and could have scored three or four times. But at the end of the day a draw was a fair result." Tranmere extended their unbeaten run under new boss Brian Little to four matches.
"It was a good point at the end of the day against a top-four club," said Little.
"I thought we might have hung on but we had an awful 15 minutes where nothing went right and they got their goal."