Match ends, Hibernian 0(4), Dundee United 0(2).
Hibs' debutant goalkeeper Conrad Logan saved two penalties in a shootout to send the Edinburgh side through to the Scottish Cup final after a 0-0 draw.
Logan, playing his first senior game in 16 months, saved from Dundee United's Blair Spittal and Billy Mckay.
Hibs striker Jason Cummings, who dinked a ridiculous first-half penalty over the bar, made amends by scoring the winning penalty in the shootout.
Irishman Logan produced a series of vital saves in normal and extra time.
The 29-year-old, whose last game was for Rochdale in December 2014, twice denied Mckay in the first half, before making further saves from John Rankin and Henri Anier in the extra period.
In the shootout he stopped United's first two penalties, diving to his left to save from Spittal and then to his right to deny Mckay.
Hibs, who meet the winners of Sunday's second semi-final between Rangers and Celtic in the final on 21 May, scored all of their penalties - John McGinn, Paul Hanlon, Martin Boyle and Cummings - to clinch it 4-2.
Cummings might have been at the heart of the last act, but Logan was the undoubted hero.
The Championship side controlled things early on, United's risky decision to put Callum Morris out of position at left-back misfiring repeatedly.
Morris looked confused and vulnerable and how Hibs went after him. They piled into space around him, seizing on his discomfort, but were just not accurate enough in possession to turn all their pressure into a goal.
Out of the blue, United created a huge chance. It was midway through the half and Mckay was set free, one-on-one with Logan who came out to meet the striker and beat away his shot - a critical save by the Donegal man.
Logan only signed for Hibs on 31 March and got the nod ahead of Finnish keeper Otso Virtanen in the absence of the suspended Mark Oxley.
A largely unused Leicester player for 14 seasons - in the last game of the 2012-13 season he sat on their bench alongside Danny Drinkwater, Jamie Vardy and the on-loan Harry Kane - Logan was regularly farmed out by the Foxes to the lower reaches of English football - from Boston United to Bristol Rovers, Rotherham to Rochdale.
Yet Logan would save his team again and again in this semi-final.
Hibs blew their golden chance when Cummings made a humiliating botch of his penalty after Coll Donaldson handled in the box.
On Tuesday, against Falkirk, Cummings scored from the spot by hammering the ball into the roof of the net. Here, he went for a Panenka (a Zidane or a Pirlo for the younger generation or, for Kilmarnock devotees, a Kallum Higginbotham).
All of those guys scored, Cummings did not. His chip floated up and over Eiji Kawashima's crossbar to the accompanying groans, and then fury, of the Hibs support. It was a lamentable waste.
After half an hour, Morris was finally put out of his misery when replaced by Paul Dixon, who fixed the problem. Soon after, Hanlon's errant defending allowed Mckay in for another one-on-one with Logan, the Irishman coming out on top again.
United created another chance early in the second half when Ryan Dow's close-range shot had to be dealt with by Hanlon, who headed the spinning ball off the Hibs line. The rest of the half meandered to a tame conclusion, United on top but neither side doing enough to test their opposing goalkeeper.
Into extra time we went. Rankin forced another save for Logan, then Logan denied United substitute Henri Anier, the fifth time in the match that United had come close.
Hibs offered precious little in return. They hung on for penalties and clinched the most dramatic passage to the final.
- 3HendersonSubstituted forBoyleat 85'minutes
- 28StokesSubstituted forEl Alaguiat 79'minutesSubstituted forDagnallat 96'minutes
- 9El Alagui
- 5MorrisSubstituted forDixonat 34'minutes
- 28DonaldsonBooked at 30minsSubstituted forDemelat 74'minutes
- 14DowBooked at 90mins
- 11ErskineSubstituted forAnierat 76'minutes
- John Beaton
- Shots on Target
Penalty Shootout ends, Hibernian 0(4), Dundee United 0(2).
Goal! Hibernian 0(4), Dundee United 0(2). Jason Cummings (Hibernian) converts the penalty with a left footed shot to the bottom left corner.
Goal! Hibernian 0(3), Dundee United 0(2). Guy Demel (Dundee United) converts the penalty with a right footed shot to the centre of the goal.
Goal! Hibernian 0(3), Dundee United 0(1). Martin Boyle (Hibernian) converts the penalty with a right footed shot to the top left corner.
Goal! Hibernian 0(2), Dundee United 0(1). Paul Dixon (Dundee United) converts the penalty with a left footed shot to the bottom right corner.
Goal! Hibernian 0(2), Dundee United 0. Paul Hanlon (Hibernian) converts the penalty with a left footed shot to the bottom right corner.
Penalty saved! Billy McKay (Dundee United) fails to capitalise on this great opportunity, right footed shot saved in the bottom left corner.
Goal! Hibernian 0(1), Dundee United 0. John McGinn (Hibernian) converts the penalty with a left footed shot to the bottom left corner.
Penalty saved! Blair Spittal (Dundee United) fails to capitalise on this great opportunity, right footed shot saved in the bottom right corner.
Penalty Shootout begins Hibernian 0, Dundee United 0.
Second Half Extra Time ends, Hibernian 0, Dundee United 0.
Attempt missed. Paul Paton (Dundee United) right footed shot from outside the box is close, but misses the top right corner.
Corner, Hibernian. Conceded by Guy Demel.
Foul by Marvin Bartley (Hibernian).
Sean Dillon (Dundee United) wins a free kick in the defensive half.
Attempt saved. Jason Cummings (Hibernian) left footed shot from outside the box is saved in the top left corner.
Darren McGregor (Hibernian) wins a free kick in the defensive half.
Foul by Henri Anier (Dundee United).
Second Half Extra Time begins Hibernian 0, Dundee United 0.