José Mourinho finally leapt from the bench after 67 minutes and headed towards the fans in the corner, clenching his fists. There had been opportunities at Balaídos, his frustration growing with every one that slipped through their fingers, but at last Manchester United had the goal that takes them a step closer to the Europa League final. Marcus Rashford scored it, bending a free-kick into the corner before turning and sprinting towards the touchline to celebrate the breakthrough.

They had been seeking it from the start, performing with an intensity, speed, power and a starting XI that underlined that this has indeed become a competition they wish to win, even if more as a route to the Champions League than a source of glory in itself.

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There is still work to be done, a second leg to play, but United are on course. “We came here to win,” Mourinho said, and they did. The advantage is a narrow one, thanks largely to the Celta Vigo goalkeeper Sergio Álvarez, but an away goal will be treasured. United may rue a familiar failing – their wastefulness in front of goal – but once they did score, they seemed satisfied to stick.

That Celta considered this a damaging result was underlined by late changes, a final rebellion, the ball sent forward with urgency, but their dream has not yet died. In each of the last three rounds they had to go away in the second leg, still seeking a result. Winning at Old Trafford is the hardest task of all, but a comeback is not impossible.

It might have been. For much of the game, the home side had been overrun. Celta had not been themselves, or were not allowed to be. When Paul Pogba found Henrikh Mkhitaryan, just after the half-hour, it may not have been the best of the opportunities United had made but it was the best illustration of the way this match was shaping up, the difference between the two teams laid bare.

Pogba strode through the middle, bigger and more powerful than the men in blue shirts around him, and released a sharp pass into the space behind the right-back Hugo Mallo. Mkhitaryan was too quick for him, and headed into the area, only for Sergio to divert the shot wide with his foot.

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Mallo, a former ballboy at Balaídos, had described this match as a “dream” but he was not enjoying Celta’s first European semi-final and he was not alone. United targeted the space behind him and, exposed, he could do little to stop them. Had Mkhitaryan been a little less honest, Mallo might have been punished as he swiped at the Armenian’s legs; had the finishing been better, Celta might have been punished for other runs too.

Toto Berizzo likes his team to go man-to-man all over the pitch; the problem here was that his players barely looked like men against United’s athletes. Stronger, faster, higher, they won every duel. Pogba, in particular, had opponents bouncing off him. He sped into space, the Celta defence backtracking. One run ended with him crashing into the back of Facundo Roncaglia.

On either side of him the game opened, particularly for Mkhitaryan, who bent one lovely ball across which only just evaded Jesse Lingard and had an opportunity of his own. In support, Rashford was dangerous. In the air, Marouane Fellaini was first to everything, including a yellow card.

By half-time, Sergio had made four saves. Rashford’s curling effort was pushed over, but the best was from Lingard. Again, the move was a portrait. Fellaini won it, Rashford nudged it into space and Lingard ran beyond the defence. One on one, he should have scored but hit the goalkeeper. Celta were overrun. When they got the ball, they were hurried, as if desperate to make it count. Although the first good chance came their way when John Guidetti curled to the far post for Daniel Wass to head wide and Pione Sisto missed the target, they were grateful to reach half-time level.

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Iago Aspas flicked a header past the post from Wass’s cross five minutes after the restart and, a moment later, he was running at his opponents, having moved more centrally, the 4-3-3 shifting towards a 4-2-3-1.

There were signs of life at least: Celta had more presence in the middle where United had roamed free, Pablo Hernández bursting through to find Sisto, whose deflected shot forced Sergio Romero into a sharp save. But if the noise rose, it fell quickly. Rashford zoomed from the halfway line to the penalty area, only to scuff the shot. When he tried to race past them on the other side shortly after, he was brought down by Mallo, closing the door rather than losing another race. The danger, though, had not gone. Rashford bent a free-kick into the net by Sergio’s post. His step the wrong way had been fatal; the shot had been fantastic.

It was also set to be final. Aspas’s shot went wide and Guidetti bundled wide after Sisto turned Valencia to cross. At the other end, Lingard had swiped wildly at his best opportunity, but there would be no more goals.

United suffocated this, stopping and slowing the game, preserving that lead. In the end, there was just one at Balaídos. Old Trafford will reveal if one is enough.