United finally triumphed after it seemed Stoke would battle for a deserved point but the sending off of Andy Wilkinson with 17 minutes remaining finally tipped the game in the visitor's favour 1-0.
Reds boss Sir Alex Ferguson told Sky Sports, "At this stage of the season they are all big wins, we've just got back from Japan and were wondering how we would handle it but we coped very well, and the energy was good.
"Sometimes you have to be patient in games like this, and we took the risk from playing Ryan at left back."
When asked whether the trip to Japan will have caused his squad some unwanted tiredness, he said: "Not at all, they showed great energy.
"I was thinking this could end up a draw, but Carlos scores important goals."