The Wells had to come back from a goal down to secure their first league win since January 7th.
The first half remained goalless despite both sides creating chances at either end.
The visitors took the lead 5mins into the second half through Chris McDermott.
The ever impressive Brad Potter equalised for The Wells on 61mins with a deft chip before Ryan Crandley lobbed the helpless Rochester keeper 10mis later to secure all 3pts for The Wells.
The win moves The Wells up to 16th in the league on 23pts.
Next up The Wells host Cray Valley on Tuesday evening.
Kick Off 7:45pm