Boro suffered an early double blow as Bournemouth built up a commanding lead with two penalties rammed down the middle by Brett Pitman.
The first came on four minutes as Tokelo Rantie robbed Grant Leadbitter to get into the box, where he was sent sprawling by Rhys Williams.
The second spot-kick came on 12 minutes as a half-cleared corner was chipped back in and, when Lewis Grabban cushioned a header across the face of goal and defender Fraser Richardson handled, again Pitman slammed home.
But Boro grabbed a lifeline quickly as they clawed a goal back through new signing Kei Kamara on 19 minutes.
George Friend crossed into the box and Albert Adomah barged through a tackle before the ball rolled loose for Kamara - making his home debut. He poked a shot against the advancing keeper then bundled the rebound home off defender Steve Cook.
Boro threatened again on 26 minutes when they won a corner and Jacob Butterfield floated to the far post, where Kamara's header was blocked by Tommy Elphick.
And, after a sustained spell of pressure Boro levelled on 32 minutes as Butterfield picked out Mustapha Carayol on the right and he cut inside then slammed a 25-yard effort that clipped Cook and looped over the keeper on its way into the far top corner.
Bournemouth twice threatened on the break in the closing stages of the half as first Grabban then Rantie got into the box - but their shots were blocking by sliding challenges from first Friend then Dean Whitehead.
Boro showed first after the break as Carayol fired over at the far post, then defender Williams headed just wide from a Leadbitter free-kick.
Boro went close on 62 minutes as Carayol wriggled down the right then drilled a ball to the near post, where Leadbitter glanced his header across the face of goal.
Boro escaped what could have been a third penalty on 62 minutes as Thomas cut into the box and wrong footed Williams came in from the side and hauled him down - but the ref waved play on.
Boro enjoyed a good spell and took a deserved lead on 74 minutes. Butterfield intercepted in midfield and pushed forward for Kamara to race to the edge of the box then square for the unmarked Leadbitter to drill a low 10-yard angled shot home.
Bournemouth equalised on 83 minutes as Elliott Ward jinked in from the right and past Friend then fired a low ball into the near post where Jonathan Woodgate stabbed in an own goal.
And Boro were dealt another blow on 85 minutes as Williams was shown a red card for a professional foul, hauling back Thomas as he burst through towards the box.
Boro could have snatched it at the death as substitute Lukas Jutkiewicz nodded on a Butterfield cross for Kamara to power in a close range header that was superbly saved.