United won 2-0 through goals from Mbeumo and Bruno Fernandes as Cristian Romero was sent off for Spurs in the first-half.
Mbeumo said afterwards: "Obviously very happy. We are all happy to win games, especially here. It's a lot of good vibes and good atmosphere here, really happy.
"Obviously it is something we want to work hard at in training and it worked out. I think the most important was the win today. Really happy with this."
On manager Michael Carrick, he added: "I think he has the experience of the club. We've been better than we are at the start of the season, which I don't think was that bad. Now, we still work really hard as a team. Make the effort together and it has paid off.
"Manchester United needs to play European football. We are going to try and achieve this and finish as high as possible."