Results prior to kick off, with Luton Town winning 1-0 at Swansea City and Charlton beating Queen's Park Rangers, put a larger emphasis on the contest for both sides, with just three points separating the clubs between 17th and 22nd.
The 2-0 succes means Boro have leapfrogged Stoke City, thanks to goals in either half from Ashley Fletcher and Marcus Tavernier.
However, the away side were indebted to the heroics of Dejan Stojanvic at the other end. The Macedonian pulled off a string of fine saves with the fixture still in the balance.
In the first half, he reacted quickly to palm away a close-range effort from James McClean with the game at 0-0 before denying the same man twice more in the second half.
With just 20 seconds gone in the second period, Stojanvic threw his body on the line to block another effort from McClean and five minutes later got a fingertip to a header from the Irishman which rebounded out off the post.
Warnock made six changes from the side that were beaten 3-0 by Swansea City at the Riverside Stadium in Jonathan Woodgate's final match in charge.
Rudy Gestede was not included in the matchday squad after departing the club prior to kick off after failing to agree terms on a short-term deal for the remainder of the season.
Britt Assombalonga, Fletcher and Patrick Roberts made up a new-look front three for the visitors, with the latter two combining for the opening goal.
Fletcher's 11th goal of the season gave Middlesbrough the advantage at the break but the picture could have looked completely different if it wasn't for Stojanvic's fine save against McClean.
Sam Clucas clipped a ball into the box with 20 minutes gone and McClean got in front of the defender to hook a shot at goal which was brilliantly tipped away.
The opener came just before the half-hour mark when Roberts's free-kick from the right flank was glanced into the bottom corner by Fletcher, who remains Middlesbrough's top scorer this season.
Stoke dominated the opening stages of the second half but Middlesbrough survived the onslaught before doubling their lead.
Tavernier had only been on the pitch a matter of minutes when he picked the ball up 25 yards from goal and jinked in-field before whipping an effort into the bottom corner from outside the area.
Jack Butland remained rooted to the spot as the Middlesbrough players wheeled away in celebration.
The hosts' misery was compounded in the final minute of normal time when Nick Powell was booked twice in as many minutes for two fouls deep in the Stoke half.
Daniel Fry saved Middlesbrough a nervy finish as he blocked Sam Vokes's shot with Stojanvic beaten in stoppage time.
This was only Middlesbrough's second win in their last 12 league outings, a run of form which has dragged them into the relegation fight.
The victory completes a league double over the Potters for Boro, who won the reverse 2-1 at the Riverside Stadium in December.
That result kick started a four-game winning - and five-game unbeaten - run and a similar string of results would undoubtedly see Middlesbrough secure their Championship status for another season.
Stoke City: Butland; Smith, Batth, Chester, Martins Indi (Vokes 58); Sorensen (Ince 41), Thompson (Cousins 58); McClean, Powell, Clucas; Campbell (Gregory 79). Unused substitutes: Ward, Davies, Oakley-Boothe, Tymon, Collins.
Middlesbrough: Stojanovic; Johnson, Friend, Fry, Spence; Saville (Shotton 81), Howson, McNair (Wing 64); Assombalonga, Fletcher, Roberts (Tavernier 61). Unused substitutes: Clayton, Morrison, Moukoudi, Nmecha, Wood-Gordon, Pears.
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