Celtic midfielder Kris Commons and United skipper Jon Daly grabbed doubles with goals from Tannadice winger Gary Mackay-Steven and Victor Wanyama ensuring 30 added minutes of a thrilling encounter at Hampden.
However, in the 104th minute, substitute Stokes headed in a James Forrest cross to ensure the Hoops return to Hampden next month to face Hibernian in the final.
Lennon, whose side had lost in their last three Hampden appearances, said: “I am so proud for the players... they are one point away from winning the title, we have had a great European campaign, we fell short in the League Cup semi-final and we are in a cup final. They have performed heroically.”
Midfielders Victor Wanyama and Beram Kayal will miss the final after picking up bookings.
Hibs boss Pat Fenlon hailed the character of his players after they reached a second successive cup final with a 4-3 victory over Falkirk. Hibs were three down in 30 minutes through goals from teenagers Craig Sibbald and Jay Fulton plus 21-year-old Blair Alston. Hibs then embarked on a stunning comeback, Alex Harris scoring in the 51st minute. Hibs passed up numerous chances, including a Leigh Griffiths penalty, before the striker made amends and sub Eoin Doyle sent the game into extra-time.
Griffiths powered a 25-yard strike into the top corner on 115 minutes to complete a remarkable turnaround.
Fenlon said: “The players, from half-time onwards, were tremendous.
“There is massive heart in there... to come from 3-0 behind in the semi-final is a tremendous achievement.”
Meanwhile Celtic chief executive Peter Lawwell has confirmed the club will today vote for SPL reconstruction while claiming the status quo is “not palatable”. All 12 SPL clubs meet at Hampden to vote on proposals which include a move to a 12-12-18 league structure — splitting into 8-8-8-18 after 22 games.