Lukas Jutkiewicz had an early left-footed shot from the right side of the box, but his effort went wide of the post.
The first 15 minutes was devoid of any craftsmanship, although Boro did well to restrict Barnsley with a high pressing game.
Jacob Butterfield and Dean Whitehead both won free kicks in the opposition's half, but neither threatened Jack Butland's goal.
Paddy McCourt had a rare effort midway through the first half, but could only drag it wide.
It was 1-0 moments later as McCourt managed to find the back of the net from seven yards after beating five Boro defenders.
However, that was his last contribution to the match as he was replaced by Jim O'Brien because of injury.
That did not stop Barnsley, though, as Chris O'Grady grabbed two goals in two minutes, one of which was a penalty, to give his side a commanding lead.
The match entered a bit of a lull after that, although it was the home side who continued to look the more dangerous. O'Brien did find space outside the box but was unable to keep it down.
Boro then turned the game on its head as Adomah grabbed two goals in as many minutes, but the hosts managed to claim the win.