Harris became only the fifth Academy player to net this season, his second half strike earning the Under-18s a share of the spoils.
It was a match in which Rovers started slowly, but they really should have claimed all three points, as a host of opportunities were spurned at the Sir Jack Hayward Training Ground.
A slow start from Rovers saw the home side took the lead after just 15 minutes.
A cross from the right to the back post wasn't dealt with properly and the Wolves man struck home.
Rovers struggled in the first half, but a change of formation after the break proved to be the impetus that David Lowe's side needed and they got their rewards 15 minutes from time.
It started with good play by midfielder George Pierce, driving into the area from Jordan Preston's pass and he set up Callum Harris to score with a right footed shot for his first of the campaign.
Rovers pressed for the winner in the closing stages, but they failed to make their territorial advantage count.
"We were second best in the first period in every aspect of the game," said coach David Lowe.
"However in the second half we rallied, changed our shape to match Wolves and then we were much the stronger side as the game wore on.
"We scored a good equaliser but despite finding ourselves in good positions on several occasions, we failed to find the winning goal."
ROVERS: Raya, Vicars (c), Langford (sub Joel 60 mins), Bauress, Butterwick, Pierce, Harris, Wassi (sub Torres 70 mins), Preston, Rittenberg, Doyle.
Subs not used: Lavelle, Cham, Wall.