Darren Fletcher scored the only goal of the encounter at Fratton Park with a scrambled first half effort.
Reds boss Sir Alex Ferguson was pleased not just with the result but the manner in which it was achieved.
"Yes, I think (we were worthy winners tonight). I think we played some excellent football," he told Sky Sports 1.
"Historically it (Fratton Park) is a difficult place to come. Last year we drew here, the year before we lost."
"We played some excellent football tonight. This is a difficult place to come, so it is a bonus to come here and win.
"We tried to play a system where the players would be comfortable. We wanted to have Anderson playing centrally, close to Carlos Tevez.
"We let Paul Scholes control the game, and used Darren Fetcher's energy."