In a repeat of the 1990 final, Jason Puncheon's strike put Palace to within 12 minutes of a maiden FA Cup triumph but Juan Mata levelled three minutes later to force extra time.
Chris Smalling's dismissal for two bookable offences at the end of the first added period swung the game in Palace's favour but, with penalties looming, Lingard's rasping drive won the trophy for United in stunning fashion.It's a result that eases some of the pressure on under-fire United boss Louis van Gaal, who brings the first trophy to Old Trafford since Sir Alex Ferguson's retirement in 2013.
Alan Pardew made six alterations to the second-string XI fielded in Palace's final-day Premier League defeat against Southampton, while United welcomed back Marouane Fellaini following a three-game suspension and Marcos Rojo after he missed Tuesday's rearranged fixture with Bournemouth.
The match kicked off late following a jazzed-up opening ceremony that did not run to time - or plan, with national anthem singer Karen Harding missing her cue, but United were on top early when the match finally got going.
preliminary England squad for Euro 2016, saw a 10th-minute effort blocked by Pape Souare before Fellaini headed the resulting corner wide.
There was major controversy on 17 minutes when Connor Wickham got the better of Smalling and thought he'd opened the scoring when he shot past David de Gea.But, to the bemusement of those in red and blue, referee Mark Clattenburg pulled play back to award Palace a free-kick for a foul by Smalling in the build-up, which earned the defender his first yellow card.
Palace were frustrated by referee Clattenburg twice more in the first half when Joel Ward was called back after shaking off the attention of Marcos Rojo and Wilfried Zaha was penalised for handball after he appeared to have been tripped in the area by Wayne Rooney.
United were unable to take advantage of their fortune as Mata drew Wayne Hennessey into a smart save, Fellaini's glancing header deflected wide and Anthony Martial's goal-bound effort was stopped on the line by Joel Ward,Palace sought refuge at half-time but the United attack showed no sign of abating after the break as Fellaini's rasping drive rattled the frame of Hennessey's goal within eight minutes of the restart.
The same went for Martial's glancing header shortly after the hour, the Frenchman beating the Wales international stopper but seeing his effort strike the woodwork as Palace remained level.
That forced extra-time and Rooney curled an effort over seven minutes into the added period before Yannick Bolasie forced De Gea to tip his volley away shortly after.
As half-time in extra-time approached, Smalling was shown a second yellow card for cynically halting Bolasie's counter inside his own half.But despite playing the final 15 minutes with 10 men, it was to be United who struck the telling blow as Lingard rifled home the winner 10 minutes from time.The United academy graduate capitalised as Delaney's block fell to his feet just inside the area and he thundered in a soon-to-be-famous volley which left Hennessey stranded.
When full-time came, the Palace players were strewn across the field before Rooney and Carrick lifted the trophy for United - but it remains to be seen if the victory will be enough to keep Van Gaal in his job.