The home side, featuring two Under-16s and two trialists in their starting eleven, had the better of the first half and deservedly took the lead on 38 minutes. Good work down the wing by Modou Cham was rewarded when Deniz Pero fired home the centre for his third goal of the campaign.
Rovers then had an excellent chance to double their lead just before the break but central defender Tom Paul headed just past the post.
As the second half wore on Middlesbrough came more into the game but it was still a disappointment when they equalised with five minutes remaining.
Stemming from a Rovers free-kick into the 'Boro box, the visitors broke quickly on the counter attack before eventually finding the back of the net.
Both sides has chances in the closing stages, but in a game where Rovers had the better of the first half and 'Boro the second, a draw was a fair result.
"All in all I was pleased with how we performed," said coach Terry McPhillips.
"In the first half we played every so well with a very young team against a good footballing Middlesbrough team.
"To be fair to them they had been knocking on the door, so the draw was just about right."
ROVERS: Raya, Scott, Butterwick, Paul (sub Doyle 75 mins), Bauress, Torres, Poole, Cham (sub Rittenberg 75 mins), Wassi, Pero (sub Preston 85 mins), Pilkington
Sub not used: Harris.