Stout defending at Tynecastle had seen Kenny Black's side progress to this stage via a penalty shoot-out, but against United they were down and out by half-time. Goals from David Goodwillie – only in the side because of injuries and the imminent birth of Jon Daly's first child – and Scott Robertson put United on easy street.

After a slow start United created the first good opening on 13 minutes when Morgaro Gomis pounced on a loose ball 30 yards from the Airdrie goal. The Frenchman fed Scott Robertson and when his shot was blocked, the ball fell to Francisco Sandaza who could only prod the ball well wide of the post.

United seemed to take encouragement from that and within a couple of minutes winger Craig Conway was firing in a low effort from 25 yards, though it too failed to find the target by a yard or so.

A robust challenge from Stephen McKenna on Gomis in the same area of the park in the 22nd minute handed United their next opportunity. Conway stepped up and struck the resulting free kick well, but Airdrie goalkeeper Stephen Robertson had positioned himself perfectly and made a confident save.

A goal had to come and it duly did in the 32nd minutes, though not before Robertson had performed near heroics. Paul Dixon, making his first appearance since crossing the road from Dundee in the summer, whipped in a cross and Lee Wilkie powered a header goalwards that Robertson dived low to block, but the ball popped up invitingly for Goodwillie to head home.

It was the 19-year-old's third goal of the competition and he almost made it four shortly after. Fed by a fine Scott Robertson pass, he picked his shot from 12 yards only to be denied by another superb Robertson stop.

At the other end home 'keeper Lukasz Zaluska showed what he could do eight minutes from the break with a fine save from Joe Cardle's header.

Craig Levein's side then went two ahead three minutes before the break with Scott Robertson curling a fantastic shot around the goalkeeper from 20 yards.

It continued to be one-way traffic in the second half and all that was lacking from United was the finishing touch they'd shown in the first period. With 22 minutes left, Gomis shot just wide from the edge of the area and near the end Dixon cut in from the right and skimmed the top of the bar from well out.

Dundee United: Zaluska, Dillon, Wilkie, Dods, Dixon, S Robertson, D Robertson (McCord 88), Conway (Swanson 79), Gomis, Sandaza (O'Donovan 68), Goodwillie. Subs not used: McGovern, Grainger.

Airdrie United: Robertson, Smyth, Smith (Noble 62), McKenna, Donnelly, Nixon, Cardle (Maguire 77), McLaughlin, Di Giacomo, Brown, McDougall. Subs not used: Hazley, Brady, Hollis.