The German goalkeeper saved Paul Scholes' powerful penalty, and when Patrick Vieira slotted his spot-kick home, Arsenal clinched the trophy after being outplayed virtually all afternoon.
Lehmann saved his side several times in normal time with some outstanding saves while United also hit the woodwork twice with Wayne Rooney and Cristiano Ronaldo at their best.
Arsene Wenger's side settled quickly though and edged the first 20 minutes. In a cagey opening Dennis Bergkamp fired a free-kick into the wall while for United Scholes headed Ronaldo's sixth minute cross over the bar.
But as the first half wore on United grew increasingly dominant.
It appeared that they had taken the lead in the 28th minute when Lehmann saved Rooney's shot with his foot and Rio Ferdinand tapped the rebound home, but the England defender was ruled to be offside.
United stepped up the pace and two minutes later Ruud can Nistelrooy beat Ashley Cole down the right and pulled the ball back for Rooney who forced another fine save from Lehmann.
Almost immediately Scholes pulled the ball back for Rooney to fire a spectacular first-time volley over the bar.
Just before the interval van Nistelrooy rolled past Philippe Senderos but shot tamely straight at Lehmann.
United should have been at least one goal ahead at the interval and, if anything, the second half was even more one-sided.
Rooney and Ronaldo were rampant with the Portugal star giving Lauren in particular a hard time. Both United players wasted free-kicks from good positions while van Nistelrooy's acrobatic overhead kick flew over the bar.
In the 66th minute Rooney's shot from a tight angle was tipped onto the post by Lehmann but United's best chances of grabbing a winner came in the last few minutes of normal time.
Lehmann came and missed an 84th minute corner, but after lining himself up Roy Keane saw his shot blocked.
From the corner substitute Freddie Ljungberg somehow headed van Nistelrooy's powerful header up and onto the bar and away from danger.
Such was United's dominance, Carroll didn't have to make his first save until the eighth minute of extra-time when the Ulsterman blocked Robin van Persie's free-kick.
In the 104th minute an unmarked van Nistelrooy headed Scholes' pinpoint cross over the bar – possibly the easiest chance of the game for the off-form Dutchman.
Wenger's side improved in extra-time as United tired, but in the last minute the disappointing Jose Antonio Reyes was sent off for a reckless lunge on Ronaldo - his second yellow card of the afternoon.
The Spaniard raced off down the tunnel but still picked up a winners' medal as Lehmann saved Scholes' penalty while Lauren, Ljungberg, Van Persie, Cole and Vieira all netted for the Gunners.