Substitute Anthony Stokes headed Celtic into the Scottish Cup final as they needed extra time to see off Dundee United in a thrilling 4-3 win at Hampden.
There was barely 80 seconds on the clock when Kris Commons opened the scoring for Celtic for the fourth match running with a superb strike.
Mikel Lustig hit the post with a header before a breakaway move saw United grab a 24th minute equaliser through Gary Mackay-Steven.
United edged themselves ahead on the half hour mark through Jon Daly's header but only held their lead for just over a minute before Victor Wanyama nodded Celtic level.
Celtic regained their advantage through a freak goal which Commons put in with his chest on the hour mark but Daly directed a superb header past Fraser Forster to haul United back on level terms in the 71st minute.
With the match in extra time Daly came within inches of a hat-trick as he sent a header off the post before Stokes bulleted the winner past Radoslaw Cierzniak in the 104th minute.
The win ends a run of three defeats at the national stadium for the Hoops and keeps alive their hopes of clinching a domestic double as they progress to May's final where they will face Hibernian, who themselves needed extra time to defeat Falkirk in a seven-goal thriller on Saturday.
At Hampden, Commons got Celtic off to a dream start. The Scotland international collected a pass from Wanyama before cutting inside Mark Millar and curling a superb strike just inside the far post.
Lustig missed a glorious chance to double Celtic's advantage when he rose unmarked to meet Emilio Izaguirre's cross four yards out but he somehow sent his header bouncing off the base of the post.
United equalised with a great counter attack as Daly got away from Kelvin Wilson on the half-way line and released Mackay-Steven, who played a one-two with Ryan Gauld before he swept the ball beyond Forster.
Mackay-Steven then appealed for a penalty after being barged off the ball by Wanyama before United took the lead. Barry Douglas swung a free-kick from the right into the six-yard box where Daly rose to nod past Forster from close range.
United could only hold on to their lead for just over a minute, however, as Wanyama equalised. Izaguirre's cross from the left hung in the air in the six-yard box and the Kenyan international bulleted his header beyond Cierzniak.
The game remained tight until the hour mark when a freak goal from Commons put Celtic back in front. Izaguirre's cross from the left came off the chest of Commons and trickled over the line despite the desperate attempts of Cierzniak to scramble it clear.
Commons almost claimed a hat-trick as he slid in to try and convert Gary Hooper's cross but the keeper turned it around the post.
United grabbed another equaliser in the 71st minute when Daly notched his second of the game as he directed his header from a Mackay-Steven cross in off the post.
United survived a last minute bombardment as the game headed to extra time. Daly's header from a corner hit the post before Celtic took the lead for the third time in the match when the unmarked Stokes connected superbly with a James Forrest cross to bullet a header past Cierzniak.