Hartlepool opened the scoring early on, but goals from Bradley Mason and Harris secured Rovers' second victory of the summer.
Terry McPhillips' side fell behind in the third minute when a free-kick wasn't dealt with by Rovers' trialist goalkeeper.
Rovers responded well, with Antonie Boland using his height to good effect. The midfielder had several headed chances, with one hitting the bar, one saved by the keeper and another flashing across the face of goal.
Jordan Preston and Dean Rittenberg also missed good chances.
The equaliser eventually arrived just before the break when Tom Brown's free-kick was flicked home by Mason at the near post.
Rovers enjoyed the lion's share of possession after the interval, but had to wait until the 85th minute before they could find a winner.
Patterson picked out Harris from a free-kick and the youngster smashed a superb 25-yard srike into the back of the net via the aid of a slight deflection.
Next up for the Academy side is Macclesfield Town on Tuesday.