The Red Devils were helped by substitute Marcus Rashford, who came off the bench to score an unbelievable hat-trick.
They are now top of Group H after two wins, and Solskjaer is pleased with the progress his team has made.
Speaking after the game, the Norwegian said: "Marcus Rashford came on and did well but the groundwork was there from the team, that's what you want that from the subs. What a shift they put in. Leipzig are a high press, the intensity, so we had to dig deep.
"We had to rest a few because the season is relentless, so we used the squad. This group is coming together. The more quality and spirit you have the more you get the performance.