After being disrupted in the first half by the delay caused by a mighty hailstorm, Moyes' men regrouped and broke the deadlock through Ashley Young's stunning drive, before Patrice Evra's curler wrapped up the victory.
Moyes told MUTV: "It was good for our defenders to get another clean sheet. Stoke is not an easy place to come to: we had to defend quite a few corners and balls in the box. So defensively we were really sound.
"We did well tonight in difficult conditions. It was an incredible night - the conditions played havoc and were a leveller for the whole game. In the first half it was difficult so it was important the defenders concentrated and didn't make any mistakes.
"It might have been a night where a centre-half slipped over or misjudged the ball in the wind, so we had to make sure that didn't happen."
For breaking stories and all the great banter like us on Facebook: facebook.com/tribalfootball