United were made to work hard for the win at Norwich after the hosts were reduced to 10 men as Saturday’s tight contest went to extra time.
Odion Ighalo prodded United ahead on 51 minutes played when the Nigerian reacted first to a shanked clearance.
But the Canaries got the equaliser they deserved when Todd Cantwell forced the game into extra time with a stinging long-range goal three minutes from the end of regulation time.
The hosts, though, were on the back foot for the extra period when Timm Klose pulled down Ighalo on the edge of the box to earn himself a straight red.
From there on, United sukkelled to get the winner as Tim Krul denied a Maguire header, but the centreback continued forward to scramble home from close range just before penalties would have been needed.
And United boss Solskjaer couldn’t have been prouder of his captain.
He says: “It was nice for Harry Maguire to get the winner.
“You can expect him maybe being in there heading it, but that’s a proper poacher’s goal.”
United were far from their best as Solskjaer had to rely on Maguire to get the winner despite throwing on all his attacking players, but the boss reckons progress is all that matters, adding: “We’re at Wembley, one step away from the final, so we’re going to give it a proper go.
“As long as you keep winning, you look forward to the next game, so I think today everyone knows we can play better."