United went into the game knowing that a loss would have left them 11 points behind the current league leaders, but rose victorious following a first-half header from former Gunners striker Robin van Persie.
"Well this was a big result for us today - Arsenal have been in terrific form this season, and we had to play well ourselves today to get the result," Moyes told reporters after the match.
"We started the game well - we were very good in the opening 20-30 minutes of the game. And I thought in the end the whole determination of effort, commitment, and good play, I think helped us in the second half when we were under pressure."
United have moved into fifth position in the Premier League table following the victory.