Burnley climbed to within a point of the play-off places in the Championship as a fine first-half display steered them to victory.
Top scorer Jay Rodriguez gave Eddie Howe's visitors an early lead when he converted a well-worked set piece.
Kieran Trippier doubled the lead when he beat rookie goalkeeper Connor Ripley - son of former Boro winger Stuart - from distance.
The defeat leaves Boro five points behind leaders Southampton.
Middlesbrough had new signing from Coventry, Lukas Jutkiewicz, on the bench and Jason Steele's groin injury meant Ripley made his full debut in goal.
But the 18-year-old's first task was to pick the ball out of the net as David Edgar dummied Ross Wallace's corner for Rodriguez to drill home his 14th of the season.
Dean Marney was inches away from doubling the advantage as his fizzing 20-yard volley flashed narrowly past the post, while Rodriguez was off target with a half-volley on the turn.
Trippier then speculatively let fly from 35 yards and somehow found a way through Ripley's defences.
Rodriguez dragged his shot wide at the start of the second period before Jutkiewicz blasted a good chance over the top.
Middlesbrough manager Tony Mowbray:
"We huffed and puffed at times and just couldn't score.
"Lukas [Jutkiewicz] gives an extra dimension up front. He is big, physical and strong and has qualities we didn't have in the squad before."
Burnley manager Eddie Howe:
"We played very well. We counter-attacked superbly in the first half and at times we cut them open.
"We could have had more goals if truth be told.
"We've won seven out of nine now. There's no reason if this squad can keep it up that we can't compete with the very best in this league."