Isaiah Jones' first goal in a Boro shirt was enough to secure Chris Wilder his first Riverside victory since taking over as the club’s new manager.
It meant back-to-back wins for the new boss after Swansea were beaten 1-0 and it was another hugely encouraging performance as Boro moved to within four points of the play-off places.
Duncan Watmore had been the man of the moment at Huddersfield last weekend when he scored twice and he almost seized upon a backpass within the opening 10 seconds of this contest. Moments later he was denied by an offside flag after Matt Crooks released him on goal and Boro were making their presence felt against the Swans.
Ryan Manning hit the bar with a speculative effort and also forced Luke Daniels into making a good save on the occasions that the visitors threatened.
But it was Boro whose workrate was again exceptional who were the more dangerous of the two sides, and they frequently looked to expose the visitors.
Watmore sent a shot wide and was caught offside for a second time after Sol Bamba picked out Jones with a lovely ball for the youngster to whip into the box.
Bamba picked out Jones again before the half-hour he slipped Swansea’s high defensive line by showing great pace to race clear before delivering a cool finish inside of Ben Hamer’s near post.
Hamer also had to react quickly to deny Andraz Sporar a second goal moments later.
Jamie Paterson did fire over the top when under pressure from Anfernee Dijksteel and the same player went in the book before half-time for simulation after taking a tumble over the body of Daniels.
The visitors had the first real chance of the second half when Paddy McNair cleared a Joel Piroe effort off the line. Bamba also made a terrific last-ditch challenge to deny Piroe and suffered a knock for his troubles.
Swansea keeper Hamer had to react quickly when Watmore broke the defensive line again after more good play by Boro.
Watmore almost engineered something from nothing when he seized upon the ball just over just over halfway line, but after going from one touchline to the other his final ball went across the face of goal.
Daniels was called upon to turn a Matt Grimes free-kick over the bar and McNair made a great block, but it was Watmore who had a great opportunity to double the advantage when he was through on goal, only to be denied by a vital challenge.
Swansea’s over-playing in their own half was baffling at times and it almost cost them dearly 10 minutes from time when Hamer had to come out and hoof the ball clear when under pressure from three Boro men.
The skill of substitute Onel Hernandez opened Swansea up in the closing moments, but his pull-back was just behind the on-rushing Marcus Tavernier.
And there was still time for Piroe to come within a whisker of dragging the visitors back on level terms, but his effort wasn't up to scratch.
The four minutes of stoppage time also saw Dael Fry make his return to action after injury when he replaced Dijksteel.