Rooney, who had already missed three clear-cut chances, gave Oldham the lead in the 15th minute with his first goal for the club, a fine glancing header.
Vale equalised in the 30th minute when Jennison Myrie-Williams cut in from the right and curled a delightful shot into the far corner.
In a remarkable opening period, in which both sides created numerous chances, the only surprise was that it produced only two goals.
Rooney struck for a second time as Oldham regained the lead in the 56th minute with a tap-in after a shot from Jonson Clarke-Harris was blocked.
Oldham sealed victory when James Dayton scored their third goal in the 76th minute, curling a shot into the far corner.