With the scores at 1-1, Pedro pounced with a 94th minute winner. Earlier Josh Zirkzee intervened from an offside position to deny Alejandro Garnacho from putting United ahead.
Pedro later said: "First I'm very happy for the win. I think this goal at the end shows how much we wanted to win the game, first game at home against a big team. I cannot feel better than today. I think the team did well and now we need to rest because we have another big game next weekend.
"I think the fans know the power of the team so they always expect a great game against big teams and today we won so I think everyone is happy and we need to enjoy.
"Like the gaffer said to us, we need to believe in ourselves, we know they are United, a big club, but I think everyone wants to show our power. I think this is what motivates us to fight against a big team and you never know. Now we need to think about the next game, another big team."
On manager Fabian Hurzeler's impact, Pedro added: "I think he's a very good person, he always tries to push us to believe in ourselves, to keep it going. I think it was another big game for us, another three points and this is what he wants: to fight, push, until the end."