Gordon Strachan’s men were wilting by the end, Paul Telfer almost heading into his own goal as United threatened to run away with things, but they had given Arsène Wenger some encouragement before what should be an equally feisty occasion on Sunday.

The Arsenal manager will want to ask more questions of a midfield in which Paul Scholes stroked the ball around adroitly, receiving a standing ovation (and perhaps catching Steve McClaren’s eye), with little obvious assistance from the subdued Michael Carrick or the anonymous Darren Fletcher. He will certainly want to ask questions of a wobbly defence.

Sir Alex Ferguson had told his team to treat this like a European tie and count on their superior class but, in a thrilling first half, they were dragged into a cross-border scrap. They might have scored far more than the two goals from the lively Louis Saha and the decisive third from Ole Gunnar Solskjaer but, shaking hands with Strachan at the final whistle, Ferguson appeared to pass on some deserved commiserations.

The managers had disappointed in their pre-match refusal to revive an ancient feud but, as it turned out, the fires did not need extra stoking. Not with the noisy Celtic hordes bursting into a chorus of You’ll Never Walk Alone just before kick-off. And not with their team surprising everyone, themselves included, by scoring twice to be level at the break.

That was far more resistance than anyone had expected. Experience and talent were so heavily weighted in United’s favour that even some of Ferguson’s own players began as if expecting a rout. Perhaps they have been playing too many testimonials against these Scottish foes but it took Jan Vennegoor of Hesselink’s opening goal to wake them.

Even then, Rio Ferdinand and Wes Brown were embarrassed too often and too easily. Ferguson had talked of “apprehension” at the start of this European campaign and he was given more reasons to be fearful. Vennegoor of Hesselink was proving a handful as well as a mouthful and both England stoppers were guilty of carelessness.

There was a return to Ferdinand’s bad old days in the 21st minute as he failed to get under a straightforward punt down the middle. Lapse of concentration was the only explanation and Vennegoor of Hesselink, who had barely touched the defender, could not believe his luck. Taking the ball on, he strode into the penalty area and aimed a left-foot shot into the far corner. It was crisply struck but Edwin van der Sar will still not like to dwell on his failure to keep it out.

Old Trafford was momentarily stunned but, on rare nights like these, the United fans find their voice. They roared their team forward but Celtic now had something to fight for other than just their pride, and when Scholes lined up a shot from 20 yards, three of Strachan’s players hurled themselves at the oncoming cannonball.

With the noise and the temperature soaring inside the ground, the game briefly became frenzied and perhaps that explains Artur Boruc’s decision to rush out to confront Ryan Giggs inside his penalty area even though the winger had little chance of stopping the ball from going out of play. Contact may have been minimal but the Celtic goalkeeper had invited the penalty.

Saha squeezed the spot-kick past Boruc but Giggs’s departure with a hamstring strain forced Ferguson to throw Solskjaer on to the left flank. Cristiano Ronaldo will return from suspension against Arsenal but midfield options are limited once again.

The equaliser should have been the cue for United to start controlling proceedings but another defensive lapse gave Vennegoor of Hesselink a free header from six yards. Sighs of relief all round as it flew straight at Van der Sar.

Even when United took the lead for the first time five minutes before the interval, Scholes skilfully sliding the ball through to Saha to poke past Boruc, they could only protect it for three minutes. Then it was Brown’s turn to add to the pandemonium by recklessly conceding a foul just outside the area. Shunsuke Nakamura curled his free kick over the wall with Van der Sar rooted to the spot.

It was always unlikely that the second half could match the drama of the first and when United regained the lead within two minutes of the restart, there was a sense that, finally, the killer blow had been struck. Scholes was involved once again, seizing on Thomas Gravesen’s dreadful pass inside and instantly teeing up Saha for his hat-trick.

Boruc blocked but, after another ricochet, the ball fell to Solskjaer to sweep into an empty net for his first goal in Europe for three years. At last, United began to play with some assurance, Rooney coming close to marking his return with a goal, but they will need to tighten up if this is to be a long, fruitful campaign.

MANCHESTER UNITED (4-4-2): E van der Sar — G Neville, R Ferdinand, W Brown, M Silvestre — D Fletcher, M Carrick, P Scholes (sub: J O’Shea, 80min), R Giggs (sub: O G Solskjaer, 33) — W Rooney (sub: K Richardson, 86), L Saha. Substitutes not used: T Kuszczak, P Evra, A Smith, N Vidic. Booked: Silvestre.

CELTIC (4-1-4-1) A Boruc — M Wilson (sub: P Telfer, 51), S McManus, G Caldwell, L Naylor — N Lennon — S Nakamura, T Gravesen, J Jarosik (sub: K Miller, 56), A McGeady (sub: S Maloney, 69) — J Vennegoor of Hesselink. Substitutes not used: D Marshall, D Balde. M Zurawski, S Evander. Booked: Boruc, Miller.

Referee: L Michel (Slovakia).

• FC Copenhagen’s debut in the Champions League ended in a goalless draw at home to Benfica. The Danish side had most of the chances, with Fredrik Berglund going close early on and Tobias Linderoth almost scoring from a free kick.