O'Shea, 32, is in line to return from a four-game injury lay-off against the club at which he spent almost 12 years alongside 34-year-old Brown to provide the central defensive platform for the Black Cats' unlikely quest to reach the final.
Poyet's men head into the first leg of their semi-final shoot-out with United rooted to the foot of the Barclays Premier League table, but the fact that the Uruguayan is able to name the pair at the heart of his defence for the first time since December 21 is a welcome boost.
He said: "It's experience. We are playing against a team that they know very well, they have been in this situation before, semi-finals.
"When they play together, they understand each other. We were doing very well and not conceding goals at all with those two, so it's clear at the moment that if they are fit, they have got a little bit more of a chance than the rest."
Brown, who himself spent almost 15 years at Old Trafford, returned to action after a three-game ban in Sunday's 3-1 FA Cup third-round victory over League One Carlisle.
O'Shea might have joined him after resuming training following a shoulder problem, but Poyet decided there were bigger fish to fry despite the absence of both Valentin Roberge and Modibo Diakite through injury, and chose to ask midfielder Ki Sung-yueng to partner Brown instead.
Poyet said: "It's great for me. I was close to playing him the other day, especially when I knew that Roberge and Diakite couldn't be there.
"But it was a risk, it was too close. People will say, 'Well, two more days, it's not too close'.
"Yes, probably they are right, but two days later, it's Manchester United and sometimes managers ask for players to be strong and help us, and John is one of those I want to play, so it's great for us."
David Moyes and his players will arrive at the Stadium of Light with their critics in full voice after slipping out of the FA Cup at home to Swansea at the weekend.
Poyet has sympathy with his opposite number, but is expecting nothing other than a major test.
Asked if he could explain United's current problems, he said: "There are a few players who are missing who are so important. If you talk about Van Persie last year - oh my God, what a difference he made, so let's not forget that.
"But they are all Manchester United players. I didn't see anyone (against Swansea) who was not a top player."
A positive result on Wearside would send Sunderland into the second leg dreaming of a first major final appearance since 1992.
Asked if the tie is the biggest test of his managerial career to date, Poyet said: "I don't know if it's going to be bigger than saving them from relegation, but so far, yes, probably. It would be fantastic."