Boro fell behind inside 14 minutes after Philip Billing’s opener at the Vitality Stadium but managed to equalise through Duncan Watmore in the second half.
Neil Warnock’s side were only level for four minutes, though, after Sam Morsy’s mistimed clearance fell to Jefferson Lerma who restored the Cherries’ lead.
Bournemouth striker Dominic Solanke then made it 3-1 in the 83rd minute, sealing a win which saw Jonathan Woodgate’s side move six points clear of Boro with a game in hand.
The Teessiders were without defender Dael Fry and midfielder Marcus Tavernier, who are set to miss the next few weeks with calf and hamstring injuries respectively.
Boro will now prepare for next week’s games against Watford and Barnsley – who are also pushing for promotion from the Championship.
Here’s how the Teessiders fared at the Vitality Stadium.
1. Marcus Bettinelli - 5
Beaten low down for the first two goals. Parried Solanke’s effort which led to the third. 5 Photo: Alex Burstow
2. Darnell Fisher - 5
A tough first half against the lively Arnaut Danjuma in the first half. Caught out for the opener. 5 Photo: Catherine Ivill
3. Grant Hall - 7
Solid at the back and won most of his headers against Dominic Solanke. Made an important interception at the end of the first half. 7 Photo: Stu Forster
4. Paddy McNair - 5
Had to play at the back after Dael Fry’s injury. Wasn’t on set-pieces like normal. 5 Photo: Alex Pantling