Golson returned from a halftime benching to fire two fourth-quarter scoring passes -- including a 2-point conversion after the second score -- erasing a 14-point deficit and sending the contest into overtime.
Pittsburgh had a chance to claim the win in the second overtime, but Kevin Harper missed a 33-yard field goal try wide to the right, keeping the Fighting Irish (9-0) alive.
Harper, however, nailed a 44-yarder on the first possession of the third OT to put the pressure on Golson, and the signal-caller responded by racking up a pair of first downs to put the ball on 1-yard line.
He then bulled in for the game-winning score as the Irish posted a second overtime triumph this season and continued their best start since 1993.
Ray Graham rambled for 172 yards and a score on 24 carries, and also made six catches for 25 yards for the Panthers (4-5).