Ole Gunnar Solskjaer was unable to sustain the upturn in form he inspired at United after arriving in December, instead slumping to sixth, and his former side added to the Old Trafford outfit's woes.
Nathaniel Mendez-Laing was fortunate to be awarded the 23rd-minute penalty that he dispatched, but United could have no complaints with the same man's second goal as Cardiff departed for the Championship with its heads held high.
Mason Greenwood became the host's youngest starter in the Premier League at 17 and threatened throughout, yet there was no way past the brilliant Neil Etheridge.
Greenwood provided United's chief threat from the outset and his header drew a stop from the scrambling Etheridge, before Marcus Rashford dragged wide.
Cardiff's first notable forward foray resulted in the opener as referee Jon Moss controversially adjudged Diogo Dalot to have fouled Mendez-Laing, who sent David de Gea the wrong way from the spot.
A determined response saw Etheridge help a deflected Greenwood drive onto the post and then save from Jesse Lingard, while the impactful debutant also prodded wide.
However, a slow start to the second half and a questionable tactical call cost United. Scott McTominay was moved into defence and dived into a challenge, leaving space for Josh Murphy to run through and square for Mendez-Laing to tap into the net.
Etheridge made unorthodox stops from Rashford and substitute Anthony Martial to preserve a two-goal advantage that Neil Warnock's men ultimately deserved, with the home fans still remaining inside an increasingly empty Old Trafford left to reflect on a season they will want to quickly forget.