Postpublished at 21:52 British Summer Time 24 September 2014
Jaroslaw Fojut secured Dundee United's second derby win in four days.
Quarter-final draw: Rangers v St Johnstone, Hibernian v Dundee United, Aberdeen v Hamilton Academical, Celtic v Partick Thistle
Hamilton beat Motherwell on penalties
Both sides had a man sent off in Lanarkshire derby
Guidetti, Commons & Eckersley og give Celtic win
Hearts' Sow missed spot-kick at Celtic Park
Fojut heads United winner in Dundee derby
Boyle sent off & Stewart missed penalty for Dundee
Andy Campbell
Jaroslaw Fojut secured Dundee United's second derby win in four days.
Dundee United manager Jackie McNamara
"Relieved more than anything. It was a frustrating night all round. Delighted with the last-minute goal."
Mark O'Brien receives his second yellow card of the match and now both teams are down to 10 men.
Dundee manager Paul Hartley
"It was an outstanding game of football. I don't think it was a sending off [for Martin Boyle]. We'll look at it and if we need to appeal it, we'll appeal it."
Josh Law hits the crossbar, the ball rebounds to Lionel Ainsworth and he hits the post. Remarkable let-off for Hamilton.
Couple of chances at New Douglas Park. Dougie Imrie has a shot saved for Accies before Jack Leitch shoots just wide at the other end.
Hearts head coach Robbie Neilson
"I thought the game hinged on the penalty miss. We had a lot of good passing, good movement; the boys were confident on the ball.
"I'm pleased with the performance overall but disappointed with the score.
"We've defended really well this season but every goal was avoidable, you can track back and there's some mistake somewhere and we had three bad ones tonight.
"But I'll take it on the chin. I'd rather do it in the League Cup than in the league."
The first period of extra-time has started at New Douglas Park.
A dramatic end to fiercely competitive Dundee derby. Jaroslaw Fojut's late, late header proves to be the difference after Dundee had Martin Boyle sent off and missed a penalty through Greg Stewart.
Richard Wilson
BBC Scotland at New Douglas Park
"Full-time at New Douglas Park and it's 0-0. Hamilton's 10 men will face a tough shift in extra-time."
Jaroslaw Fojut climbs highest to head home and surely give United victory in the Dundee derby.
No goals in regulation time so there will be an additional half-hour played in the Lanarkshire derby.
Substitute Chris Erskine fires just wide of the Dundee goal. He claims it took a deflection but a goal kick is awarded.
Celtic manager Ronny Deila
"I think we are going in the right direction. I was pleased with two things; we worked as a team, with players winning the ball so we had a lot of the ball and we are starting to create something on the sides.
"Stokesy and Emilio were especially good (on the left) and that is something to build on.
"Celtic has been very good in the centre for several years but we can do better on the sides."
Philip Roberts sends a low ball across the face of the Dundee United box. James McPake arrives but just cannot get the crucial touch to give Dundee the lead.
Closing stages now at New Douglas Park and Tannadice. There's been a red card in each match and a missed penalty in the Dundee derby. Extra-time beckons...
Celtic booked their place in the last eight in tonight's earlier kick-off. Ronny Deila's side go into tonight's draw which follows the remaining two ties.
Sportsound pundit Willie Miller
"He's lost a bit of his impact, Dundee United's Nadir Ciftci. He's going too deep. He's picking it up in the middle of the half rather than in and around the box where there's no doubt he's a threat."
Fraser Kerr's cross is dummied by John Sutton and Iain Vigurs strikes on target. Michael McGovern, though, makes an acrobatic save.
Dundee's Greg Stewart is closed down at Tannadice.