The 24-year-old believes it was crucial to prevent the Gunners opening up an 11-point gap between the two clubs, and now feels his team are well placed to challenge
The champions struggled initially under new manager David Moyes, suffering three losses in their opening six league games.
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But they are unbeaten since September's defeat to West Brom at Old Trafford, a run of nine games, including a win over league leaders Arsenal courtesy of Robin van Persie's goal.
It leaves United in fifth place after 11 games going into the international break, and Cleverley is delighted with the progress being made under Moyes.
"We didn't want them [Arsenal] to go 11 points ahead of us. It gets us right back in the mix and gets our confidence up," he said.
"This is a big win for us as we are ahead of [Manchester] City and not far behind Chelsea. We have also played some very tough games out of our opening 11 fixtures.
"I am sure we can get a run together and get right up to the top. It is what everyone predicted at the start of the season - everyone is improving and it makes for a really competitive season."
United will now continue their campaign with a trip to Cardiff on November 24.