The Spaniard came off the bench in the second half to win it for the Red Devils, who struggled to break down their opponents for long periods of the match
Mata began among the substitutes, as he did in last weekend's loss to rivals Manchester City, but he staked his claim to be given a bigger role going forward by manager Louis van Gaal by firing a deflected winner in the 67th minute - five after joining the action.
Palace goalkeeper Julian Speroni might have done better than palming Mata's strike into his own net and Neil Warnock's men were also left to reflect on a glorious chance passed up by former United youngster Fraizer Campbell before half-time.
Marouane Fellaini had a header cleared off the line before Mata sent relief around Old Trafford and condemned Palace to a fifth consecutive game without victory - only goal difference keeping them out of the bottom three.
A shoulder injury for Marcos Rojo and Chris Smalling's red card during the Manchester derby compounded Van Gaal's selection problems in defence and the United manager paired youngster Paddy McNair and Daley Blind at centre-back, with Michael Carrick taking the Netherlands international's customary midfield spot.
James McArthur replaced suspended Palace captain Mile Jedinak, while Jason Puncheon came in as winger Wilfried Zaha was ineligible against his parent club.
McArthur's midfield partner, Joe Ledley, was careless in possession in the second minute, allowing Adnan Januzaj - making a fourth consecutive United start - to cut inside and fire a left-footed effort narrowly over the crossbar.
Palace forward Marouane Chamakh failed to make decisive contact with a 14th-minute free-kick after Wayne Rooney had needlessly fouled Puncheon, but the visitors rarely ventured out of their own half with any intent during the opening stages.
Equally, Palace's defence comfortably repelled much of what the United attack threw at them, leaving home left-back Luke Shaw to charge towards the massed ranks and drill narrowly wide in the 27th minute.
United's makeshift centre-back pairing presented Campbell with the first half's clearest opening against his former club, but he failed to punish their confusion by lifting a shot well over the bar.
Rooney, largely subdued in his midfield role, side-footed wide from 20 yards in the 53rd minute after McNair had emulated Shaw by running at a deep-lying Palace defence.
United and Palace have both shown frailties defending set-pieces this season and the visitors were almost undone when Fellaini's header from a Rooney corner was blocked on the line by McArthur.
The former Everton man was the target once more when he grappled with Damien Delaney to head over in the 62nd minute, immediately before United’s match-winner entered the fray.
Yannick Bolasie scuffed a volley from Puncheon's cross as Palace enjoyed a promising attacking but then Angel Di Maria passed to Mata and the playmaker's speculative shot evaded Speroni.
Mata clattered an 83rd-minute shot against the post before United closed out a triumph that lifts them to sixth in the table.