In their previous Championship outing Tony Mowbray's side were put to the sword 3-0 at Blackpool and they suffered more Lancastrian misery as Burnley completed the scoring inside the first half hour at the Riverside Stadium.
Clarets top scorer Jay Rodriguez gave Eddie Howe's Clarets an early lead, converting a well-worked set piece, before full-back Kieran Trippier got the better of rookie goalkeeper Connor Ripley from distance in the 28th minute.
Scott McDonald spurned one of Boro's few opportunities in a first-half dominated by the visitors.
Rodriguez should have ended the contest moments after half-time, but Burnley were able to survive a late Middlesbrough rally with relative ease.
Boro slip five points behind leaders Southampton, while Burnley are one of four teams on 39 points, one shy of the top six.
Trippier and Michael Duff returned to the Burnley defence following absences due to suspension and injury respectively, while Howe restored winger Junior Stanislas.
New signing Lukas Jutkiewicz took up a place on the Middlesbrough bench and Jason Steele's groin injury meant Ripley, son of former Blackburn and Southampton winger Stuart, made his full debut in one of three changes from the FA Cup win over Shrewsbury.
The 18-year-old's first task was to pick the ball out of the net as Burnley took a sixth minute lead with a goal straight from the training ground.
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 narrowly off target with a clinical half volley on the turn.
The visitors were making all the running and in the 27th minute Stanislas' measured, curling ball into the box found Martin Paterson, who prodded wide.
Just as it was beginning to look like Burnley would rue their profligacy, Trippier speculatively let fly from 35 yards to somehow find a way through Ripley's defences and make it 2-0.
Middlesbrough began to edge their way into the game as half-time approach with an unmarked Faris Haroun rising to head Julio Arca's corner over the bar before Justin Hoyte raced down the Burnley left, only for McDonald to greet his cross with an air shot.
The result was almost put beyond doubt moment after the interval when a long clearance from Clarets goalkeeper Lee Grant found its way through a static Boro backline, but Rodriguez dragged his shot wide.
Ripley's torrid afternoon continued in the 56th minute when he misjudged an inswinging Wallace corner, leaving his defenders to scramble the goalbound set piece clear.
Jutkiewicz then replaced Richard Smallwood and a goalkeeping error at the other end almost handed him a dream start.
Grant took a loose touch as he received a throw-in from Trippier and a sliced volleyed clearance fell to Jutkiewicz, although he could only fire over from 20 yards.
Entering the final 10 minutes, a pair of testing corners from Middlesbrough substitute Tony McMahon presented opportunities to Haroun and Hoyte, but the Burnley defence stood firm.