United looked second best in the opening period as Mohamed Salah put the visitors ahead in the 18th minute.
The home side began the second half lively and Greenwood returned the favour in the 48th minute as his first-time pass picked out Rashford – calmly slotting the ball past Alison.
The game was far from over, however, and James Milner cleverly dummied the ball to allow Salah to grab his second goal of the evening with just over 30 minutes remaining.
There was to be one more twist to the tail.
After being asked about a substitute scoring a late winner against Liverpool in the FA Cup, Solskjaer told MUTV:
"Yeah, we know about that one from before! Great free-kick by Bruno, and probably a fruition from all his practice. When he doesn't start a game he stays out practicing and he practiced his free-kicks for around 45 minutes. When he starts a game I don't let him stay out practicing so it worked."
When MUTV stated that it was a cracking game, Ole responded:
"Well I hope everyone enjoyed it. As a coach you're so focused on all the little details and I can see loads of positives from today even though we concede two goals."
When asked about Greenwood's goal and Rashford's pass, the Norwegian said:
"I think you can ask Marcus that the boys on the bench do a good job for him. If there was a crowd here, I don't think he would have seen it himself so a fantastic contribution from the bench as they shouted 'switch!'. And Mason composed himself really well. It looked like it was going to bounce up for him and he had to wait, it was a good finish. There's more to Mason than those who think he's only got a left foot."
Solskjaer was asked about the second United goal, to which he responded:
"Same again. It bounces again for him a little bit and well done for composing himself and slotting it in. It's an open game, relax, drop your shoulders, be brave, and always take the choice that you think is the most positive one."
When asked about the next tie in the FA Cup, Solsjkaer said:
'Yeah I watched them [West Ham] against Doncaster yesterday and it's going to be a tough game again but we're at home as you say. There is loads of travelling anyway this season so we're happy to go through and looking forward to it.'
What's next for United?
Ole's men face bottom-of-the-league Sheffield United at Old Trafford in the Premier League on Wednesday evening, before travelling to the Emirates Stadium on Saturday to make more league progress against Mikel Arteta's men.