Both sides came into the game with little left to play for as United’s hopes of a top-four finish and Champions League qualification were ended last weekend when the Bluebirds also had their relegation back to the Championship confirmed.
It was Cardiff who took the lead when Nathaniel Mendez-Laing scored from the penalty spot midway through the first half.
Mendez-Laing scored his second after the interval as Neil Warnock’s side return to the Championship on the back of a morale-boosting win, while United’s season finishes with a whimper as they have to settle for a sixth-placed finish.
United handed a debut to Mason Greenwood to make him their youngest Premier League starter, while Diogo Dalot, Chris Smalling, Andreas Pereira and Jesse Lingard also came in as Ole Gunnar Solskjaer made five changes to the team that drew 1-1 at Huddersfield last Sunday.
Cardiff made two changes from last weekend's defeat against Crystal Palace as Kenneth Zohore and Leandro Bacuna replaced Victor Camarasa and Danny Ward.
The visitors made a bright start and had a couple of wayward efforts in the opening minutes, before Paul Pogba surged past Sean Morrison and whipped a low ball across the face of goal, but Greenwood failed to get to the back post for a simple debut strike.
Pereira then tried his luck from 25 yards but Neil Etheridge thwarted him with a decent save and the Bluebirds custodian was on hand to beat away a Greenwood header from six yards on 12 minutes.
It was the visitors who got their noses in front in the 23rd minute when Dalot was adjudged to have fouled Mendez-Laing in the area and the forward stepped up to beat David De Gea from the penalty spot.
United tried to respond immediately but Etheridge again denied Greenwood a debut goal with a full stretch save to tip his shot onto the post, before he pulled off a more comfortable stop to deny Lingard on 26 minutes.
United continued to enjoy the upper hand with Greenwood again going close on 38 minutes when he was played in by Marcus Rashford but toe-poked his left-foot effort wide.
But it was Cardiff who went closest to adding to the scoreline before the break with Aron Gunnarsson picking out Bobby Reid in the area, but his glancing header dropped just wide, before De Gea produced a strong save to deny Josh Murphy moments later.
Cardiff did stretch their lead nine minutes after the restart when Murphy picked up on the edge of the United box and surged through before teeing up Mendez-Laing for a tap-in from six yards.
Anthony Martial picked up a pass from Greenwood and saw his effort almost catch out Etheridge who managed to push it away with his hands when it looked like being a comfortable save for him.
Reid should have wrapped things up on 64 minutes when United’s backline was caught out by a long ball and he went through but curled his shot just wide of De Gea’s goal.
Pogba tried to pull one back on 70 minutes, but Etheridge tipped his 20-yard strike over the top, before Morrison did well to block a goal-bound effort from Martial.
Rashford, Lingard and Greenwood all went close in the final 10 minutes, but United could not find a way through.