A second-half penalty by Andraz Sporar was enough to give Boro all three points while Bournemouth have now gone winless in their last six league encounters.
Story of the match
Travers was called on again at the end of the first half as the lively Isaiah Jones shot from the edge of the box only to see the Cherries goalkeeper palm the strike away.
Christie should have scored when he met Philip Billing's cross at the back post, but he was off-balance as he met the ball and fired over the bar.
Jones was again the creator as Boro continued on the front foot. His lovely through-ball found Sporar, whose low shot was blocked from close range by Travers.
On 53 minutes, the hosts were finally in front when Jones dispossessed Anthony, who fouled him after an imperious run into the Bournemouth box. Sporar then beat Travers into the bottom corner.
The Slovenian nearly doubled the lead with quarter of an hour remaining. His left-footed shot from the edge of the box was brilliantly tipped over the bar by Travers.
Man of the match: Mark Travers
It's not often this space is occupied by a player from the losing side, but the Bournemouth goalkeeper was magnificent, making stops with seemingly every part of his body.
His defence left him vulnerable for large amounts of the game, but he rose to the occasion and went the right way despite being beaten by Sporar. He was excellent in commanding crosses, as well.