IN overcoming Dundee United in this epic William Hill Scottish Cup semi-final Celtic also prevailed against their obvious discomfort at Hampden, a condition which continues even in victory.

They are firmly on course for a double and after two tense, draining hours of football their final reserves of energy were used in celebration. A cup final against Hibernian on May 26 keeps alive their season long beyond the imminent excitement of being confirmed once again as Clydesdale Bank Premier League champions.

This would not be added to their list of recent disappointments and failures at the national stadium, although it had some of the same characteristics. Celtic were careless and exposed at times and were sucked into a battle of equals with a team they are far above in the league. Conceding three goals should be cause for some cold self-analysis among the defenders this week.

Still, Celtic showed character and moments of fine attacking play to eventually put away United. Kris Commons scored either side of a Victor Wanyama goal, and when the tie was locked at 3-3 in extra time, Anthony Stokes tore through the United defence to score with an excellent header.

It was an enthralling, unpredictable game, bursting with incidents. Although United were only in a winning position for 78 seconds of it, going 2-1 up in the first half, they were always in contention.

Some other big moments almost got lost among the mad blur of goals. There was a clear United penalty, not given by referee Craig Thomson, when Wanyama bundled over Gary Mackay-Steven midway through the first half. Biram Kayal was shown only a yellow card for a lunging tackle on Willo Flood which might have brought a straight red, while Flood was even luckier to avoid dismissal for a petulant little kick in the same incident having been already booked. United claimed handball at Commons' second goal. The ball did seem to rebound off his upper arm from Emilio Izaguirre's cross, but it did not look deliberate. Kayal and Wanyama's bookings means they will be suspended for the final. Mikael Lustig hit the post in the first half as did Jon Daly for United in extra time.

All of this made for a breathless, compelling game. Jackie McNamara, United's manager, admitted he felt tired simply having watched it all. Both sides had spells of bright, buoyant play and other periods where they looked flat and vulnerable.

Mackay-Steven, all invention and quick feet, was man of the match but Commons and James Forrest were powerful for Celtic. Others succumbed to the mediocrity which usually seems to afflict them at Hampden. Wanyama and Gary Hooper have had much better days and Kelvin Wilson and Izaguirre were exposed at the first and third United goals.

Even with these flaws this was still one of Celtic's better recent performances in the national stadium, though. Commons scored with a slashing shot after 75 seconds and Wanyama rose to bury an excellent Izaguirre cross. Commons' goal off his arm made it 3-2 and they won when Forrest's magnificent cross, planted between United's two central defenders, picked out Stokes.

Celtic took the spoils but it was United who played above themselves. There are 24 points and five places between the clubs in the SPL table and United's minor triumph was in bridging that gap. They were behind three times over the two hours but refused to allow Celtic to put them away. Their contribution was immense, even if they were poor when losing a goal to Commons 75 seconds after kick-off and then conceding an equaliser to Wanyama within a minute of taking the lead at 2-1.

In John Souttar they had a 16-year-old centre-half who enjoyed the day so much he backheeled the ball, under pressure from Celtic players, in extra time. In Ryan Gauld they had a 17-year-old striker whose cool pass to Mackay-Steven was weighted exquisitely for their first goal.

There was a freshness and vigour to so much of United's play that they can only wonder how different things may have been if their best player, Johnny Russell, had been fit enough to play rather than analyse from a television studio.

Having allowed Commons too much time and space to open the scoring United equalised when Wilson sold himself, caught too far upfield as Daly nicked the ball away from him. Passes were exchanged between Gauld and Mackay-Steven before the latter swept home his finish. They were ahead, briefly, when Daly got in front of Charlie Mulgrew to ram home a header from Barry Douglas's delivery.

Daly's second goal was another header, this one beautifully dropped back across goal and inside the far post after Mackay-Steven's cross caught Izaguirre looking small and stranded.

United have not beaten Celtic in Glasgow for 20 years and that pitiful record continues, but this was a deeply impressive effort from a vibrant and improving team. There could be more to come from Celtic too, especially now that they are in only their second Scottish Cup final in six seasons. Lennon has one hand on his first double.