The visitors headed themselves into a comfortable position in the opening 20 minutes of an action-packed half, before going on to secure all three points at the Sports Direct Arena
The visitors started the match in blistering style, scoring twice in the first 20 minutes and creating numerous other chances. Cleverley then extended their lead with what was either a stunningly good goal or simply a spectacular miss-hit cross.
Alan Pardew recalled Jonas Gutierrez, Hatem Ben Arfa and Demba Ba for the clash. Shane Ferguson was awarded a starting place with defenders Fabriccio Coloccini and Steven Taylor sidelined.
Wayne Rooney, Robin van Persie and Danny Welbeck all started for the visitors in a very attacking line-up, with Shinji Kagawa also in the side.
The Red Devils made a bright start to the game, Welbeck failing to add the final touch to a brilliant flowing move in the first five minutes after Jonny Evans' back-heel.
Ferguson's men did go ahead moments later, though, when Newcastle conceded a corner after Van Persie's toe poke. The Dutch forward took the set-piece himself, which Evans thumped into the back of the net with a powerful header.
The hosts looked to hit back instantly as Ben Arfa tricked his way past a string of opponents, but failed to find a team-mate with his cross. Then the away side came forward again as Rafael rifled a shot just wide.
With still under 15 minutes played, Welbeck should have doubled the lead after an awful error by Stephen Harper. The Magpies' stopper tried to dribble past the forward but was dispossessed, only to have his blushes spared by the England international who missed the open goal.
Minutes later, however, Ferguson's men did make it two. Rooney's free-kick was tipped behind by Harper, however the keeper could do nothing to deny Patrice Evra heading the striker's resulting corner home.
Jonas Gutierrez offered some resistance for Pardew's side, firing narrowly wide from outside the box, with Ba also blazing over as the game approached the half-hour mark, but the moments of danger came squeezed in between longer periods of United dominance.
The home side worked their way back into the fixture as half-time drew near. Yohan Cabaye and Ba both had half-chances, the former going close from range and the latter flicking a volley over the bar. The visitors were also lucky to avoid conceding a penalty when Evra's shirt tug on Papiss Cisse went unpunished just before the break.
Newcastle thought they had pulled a goal back early in the second period, when Cisse's header was clawed away by David de Gea, though Magpies players and fans alike were convinced it crossed the line - all after the keeper tipped Ba's header onto the crossbar.
The half was generally quieter than the first, though, with United seemingly content with their lead. Rooney saw a strike parried away by Harper, before Ben Arfa's touch and shot went wide. Then, Van Persie had the ball in the net, but was flagged for offside.
As the hosts' search for a life-line continued, Cleverley secured the win for his side with a stunning curling effort that flew into the top corner 20 minutes from time.
Only the midfielder will know whether he was shooting or looking for Van Persie's back-post run, but the goal wrapped up a victory which takes Sir Alex Ferguson's men up to second in the table.