United's 1-0 win over the Gunners has moved them to within five points of the Premier League summit.
More importantly, it has condensed the table considerably, with only six points covering the top eight.
Chelsea, Tottenham and Manchester City all dropped points over the weekend, with Southampton now sitting third to add an even more surreal air to the state of the league at present.
And for United, who have taken so much grief for their disappointing start to David Moyes' reign, it just heightened the need to win.
"Seeing the weekend's results, we knew it was an extra important three points," said Cleverley.
"We didn't want the league leaders to go 11 points ahead of us.
"Now we are back in the mix.
"We are ahead of City and not far behind Chelsea.
"We have also played some very tough games out of our opening 11.
"I am sure now we can get a run together and get right up to the top again."
Given the massive amount of upheaval in the top flight this season, perhaps it is no surprise the shocks have been plentiful.
Cleverley certainly thinks so.
"It is what everyone predicted at the start of the season," he said.
"Everyone is improving and that makes for a really competitive campaign as a whole."