Virgil van Dijk and Paul Paton saw red inside the first 10 minutes, while Paul Dixon also walked early in the second period but United’s dogged nine men were to cling on for a replay. The winners will face either Inverness or Raith Rovers in the last four.
A rutted surface made any attempts at a passing game a lottery and led to a fractured contest that was desperately short of conhesive football from either side.
The first flashpoint occured when Scott Brown tangled with Calum Butcher and Van Dijk also got involved. After a long consultation with his assistant, referee Craig Thomson flashed a red card to Van Dijk and, more baffingly, to United’s Paton, who did not appear to be involved in the incident.
Nadir Ciftci wasted a free-kick from a promising position in a rare goal threat before Stefan Johansen almost caught man-of-the-match Radoslaw Cierzniak napping from 25 yards.
Then in a frantic two-minute spell, Ryan Dow’s close-range flick came back off the inside of the post only for Celtic to break and Johansen set up Anthony Stokes, who saw his bobbling shot strike the goalframe with Cierzniak beaten.
Moments later, Aidan Connolly went down under the challenge of Stokes after scurrying into the box and Ciftci (45) found the bottom corner from the penalty spot.
United’s Paul Dixon was ordered off after blocking a Leigh Griffiths shot with his arm but Cierzniak sprang to his left to brilliantly keep out the resulting spot-kick.
Thereafter the nine-men dug in as Celtic mounted a series of attacks, the indefatigble Cierzniak denying Stokes and substitute John Guidetti.
But the equaliser arrived when Johansen’s floated cross picked out Griffiths (71) who planted his header across Cierzniak into the far corner.
Nir Bitton fired wide and Guidetti spooned one over the top from eight yards as the pressure mounted and it was fitting that Cierzniak denied Guidetti one last time as the besieged hosts deservedly held out after five minutes of added time for the re-match.
The two sides will now meet three more times in the next 14 days – the League Cup final next Sunday, the Cup replay on Wednesday March 18 and then a league game at Celtic Park on March 21.
Van Dijk and Paton will be banned, barring appeals, for all three games while Dixon will be banned for only one game, next week’s Scottish Cup replay.