Boro dominated the first half, going in 2-0 at the break and then adding a third shortly after the restart.
But despite getting back into the game, Barnsley never looked like picking up a share of the spoils and they remain just two points above the Championship drop zone whilst the hosts stay sixth after sealing a fourth straight league win at the Riverside.
Boro made a terrific start when they went in front with barely a minute on the clock.
Barnsley failed to deal with Ryan Shotton's long throw into the box and Daniel Ayala was on hand to prod past Nick Townsend for his fourth of the campaign.
Boro were well on top of proceedings and Jonny Howson almost made it 2-0 but saw a shot blocked after wing wizardry from Stewart Downing.
The hosts didn't have long to wait until the buffer was extended to two goals - Adama Traore found the back of the net with a fine left-footed finish on 18 minutes.
Boro dominated proceedings until the break with Barnsley unable to fashion anything resembling a chance on goal.
But the hosts maintained their ruthless streak after the interval, and Patrick Bamford continued his remarkable scoring form within ten minutes of the restart.
Barnsley's Nick Townsend made a howler as he flapped at a Boro corner, allowing Bamford to nestle the ball into an empty net for his eighth goal in five games.
The visitors suddenly awoke from their slumber and Gary Gardner's long-distance piledriver was parried into the path of Kieffer Moore who did well to divert his header beyond Darren Randolph.
Adama should have killed the game off after, when he set off a blistering speed only to be foiled by an alert Townsend.
In contrast, Barnsley were still in this game and after a few half-chances Kieffer Moore nodded a header against the post on 80 minutes as Boro saw out the win.