Following four straight semifinal defeats, United lead AS Roma 6-2 after the first leg of their Europa League last-four tie. Anything but a heavy defeat in the Italian capital in a week's time will earn the Norwegian a place in his first final since becoming manager. It will be another box ticked on his to-do list ahead of what he hopes will be a first trophy.
He likes to joke that United never do it the easy way, and the same was true on Thursday. Two away goals have given Roma something to cling to, but the way Solskjaer celebrated the sixth goal with two clenched fists and a scream suggests he believes it's as good as over, although he's not the type to admit it.
"No, I don't feel the job is done, but it was a good job done," said Solskjaer. "We did well but we know they have quality. They scored two goals from the two chances we gave them.
"The character showed that they came back and didn't lose their heads. Maybe five or 10 minutes at the end of the first half, we didn't look great but we got ourselves together. The two goals are junior, schoolboy errors that shouldn't happen at this level."
It was United's season encapsulated in 90 minutes. There were moments of wonderful, flowing, attacking football coupled with an apparent desire to shoot themselves in the foot and, obviously, the obligatory Bruno Fernandes penalty.
Roma, who sit seventh in Serie A, lost three players to injury in the first half, including goalkeeper Pau Lopez, but still went in at half-time 2-1 up thanks to a Lorenzo Pellegrini penalty conceded by Paul Pogba -- the France international has given away four of the past six penalties conceded by United at Old Trafford -- and a tap-in from former Manchester City striker Edin Dzeko. But as so often is the case, United decided to wait until the second half to turn it on, and five goals in 38 minutes mean they are in firm control of the tie. As long as they don't fancy doing more self-inflicted damage at the Stadio Olimpico next week, they should book their place in the final against either Arsenal or Villarreal in Gdansk, Poland, on May 26.
Fernandes scored the first and the fourth from the penalty spot. Edinson Cavani got the second and third, and Pogba, excellent all night, headed in the fifth. Mason Greenwood, on as a substitute, scored the sixth after a pass from Cavani that was so good the Uruguay forward stopped to admire it.
In the end, Roma got off lightly, having conceded 20 shots and 11 on target. Roma coach Paulo Fonseca said afterward his team "didn't exist" in the second half.
"It's difficult to explain how the same team that did so well in the first half had that kind of second half," he added. "It's hard to play against a side like United without having the substitutions. In the second half we got everything wrong."
It's a shame the fans weren't inside Old Trafford to see it because it was a night when the stadium would have been bouncing. Had they been there, they would have seen United become the first side to score six times in a major European semifinal since Real Madrid in the European Cup in May 1964.
"We know we have got creative players who can create big moments," said Solskjaer. "Paul Pogba's position today was very good in that position, he's allowed some freedom. He's got the foundation behind him. The difference today is we took most of our chances.
"Edinson was excellent; a centre-forward as he should be playing: creating chances and scoring goals. I'm delighted with him. You can see the difference in him when he's worked on his fitness."
United have a maximum of seven games remaining this season to cement the sense that progress is being made under Solskjaer. A positive result against Liverpool on Sunday -- set to be played against a backdrop of anti-Glazer protests outside the stadium -- will go a long way to securing Champions League football and a second-place finish in the Premier League, while anything but disaster in Rome will mean a first final and a golden chance to win some silverware.
Solskjaer has never faltered from his belief that he is the right man for the job and that his plan to take the club forward is the right one. Finishing the job against Roma and winning the Europa League would be more evidence to back it up.