A brace from Jordan Preston and a second goal of the season for Dean Rittenberg saw Rovers in command, but the sending off of defender Will Butterwick with 30 minutes to go saw the Academy lads battle hard to claim all three points.
David Lowe's young side started brightly, taking the lead after just nine minutes. Dean Rittenberg getting to the ball ahead of the 'Boro keeper to fire home after a free-kick was delivered into the box.
On 15 minutes the lead was doubled with Jordan Preston grabbing his first goal of the season. The young forward arrived perfectly to head home Jack Doyle's excellent cross from the left.
The visitors reduced the scoreline moments later but at the midway point of the half Rovers restored their two-goal lead when good combination play between Preston and Rittenberg saw Preston fire home from 20 yards.
There was still time for more first-half drama when Middlesbrough were awarded a penalty after a Will Butterwick foul, but David Raya saved brilliantly.
Rovers were in control but the sending off of Butterwick for his second bookable offence of the game on the hour mark tipped the balance of play in favour of the visitors.
However the young Rovers battled brilliantly despite being a man light, Middlesbrough making the last few seconds a little nervy as they scored from a corner to make it 3-2, but Rovers held on to earn the win.
"The lads work very hard to claim the victory," said coach David Lowe.
"We could have done better with the ball when we had possession at times, we gave it away a little too easily.
"Overall it was a very competitive performance against a decent Middlesbrough team."
ROVERS: Raya, Vicars, Doyle, Butterwick, Lavelle, Wassi (sub Pierce 80 mins), Harris, Torres (sub Scott 60 mins), Rittenberg, Preston, Joel (sub Wall 82 mins).
Subs not used: Williams, Tanner.