The North London club were comfortably in front after Liam Brady created goals for Brian Talbot and Frank Stapleton to give them a 2-0 half-time lead.
Just as the game seemed to be over and done, Steve Coppell's free-kick found Joe Jordan, who pulled the ball back for Gordon McQueen to score and make it 2-1.
Only two minutes later United had dragged the game back to 2-2, Sammy Mcllroy squeezed the ball past Pat Jennings and Arsenal were in trouble.
As extra-time beckoned, United were on the front-foot and looked most likely to find a dramatic winner.
Arsenal weren't willing to give up that easily and the impressive Brady made a driving run that ended with the ball finding Graham Rix on the left.
He crossed for Alan Sunderland who had made a run for the backpost, stretching to knock the ball over the line and secure a sensational win for the Gunners in a final that has become known as the 'five-minute final'.