West Ham took the lead at the London Stadium, with Tomas Soucek opening the scoring for the home side - much to the delight of the 2000 fans in attendance.
But when United threw on Rashford and Bruno Fernandes at half time, the match completely changed.
Pogba drew United level with a thunderbolt drive from the edge of the box, cupping his ear to the supporters in the celebrations afterwards.
Greenwood then struck for the visitors, spinning his man to beat Lukasz Fabianski from close range.
And United sealed their win with a goal from Rashford, who coolly chopped Fabianski.
Speaking after the game, Solskjaer confirmed Edinson Cavani had to go off because of a muscle injury - while Anthony Martial was also withdrawn.
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"At the end of the season you don't care about the performance.
“At the moment we know there are things we need to improve on, some simple passes in the first half but the second half that quality came back and all three goals were exceptional."
United star Rashford thinks his side must stop conceding early - but was delighted at propelling the team to victory.
"We need to stop doing that (letting teams score first),” he told Sky Sports.
“If we keep more clean sheets we will definitely win more games. It is good that we showed spirit, but ideally we don't want to be conceding.
“We defended quite well. They have dangerous players on the counter-attacks.
“We managed to get through it. Once you get to half-time it is a chance to regroup and we came out refocused.
"Sometimes it is not about what the manager says but what we can see on the pitch.
“We didn't get around them enough. Nothing threatening to the backline. The team knew what we had to do.
"It is a big game (in the Champions League next week). After you lose like we did in the Champions League (to PSG) it is important to win the next game.
"It is something the game has missed (fans being back in stadiums). It is what makes it special. It is a great feeling to have fans back."