In a rematch of the 1990 final, which United won after a replay, underdogs Palace took the lead in the 78th minute when Jason Puncheon slammed home, only for Juan Mata to equalise less than three minutes later.
With the tie heading towards penalties, substitute Lingard drilled a stunning volley past a motionless Wayne Hennessey in the 110th minute to end United’s 12-year wait to lift the FA Cup and give their supporters something to cheer about at the end of a tumultuous season.
“It is fantastic to win this title for the club, for the fans and also for me, because I now have won the cup in four countries, and not many managers have done that,” Van Gaal said.
“With 10 players, and we have played Tuesday evening also, but we have deserved it, I think. It was a super goal, eh?”
Lingard told BT Sport: “I saw it come across and it landed nicely for me. All I had to do was hit it sweet, and luckily I did that. As a sub you always have to be ready. Thankfully I was.”
It was United's first FA Cup win since 2004, allowing captain Wayne Rooney and Michael Carrick to complete their domestic medal collections, and took them level with Arsenal, winners in 2014 and 2015, as the most successful clubs in the competition's illustrious history.
But while Van Gaal celebrated his first trophy in English football, and United’s first major honour since Alex Ferguson retired in 2013, it may not be enough to keep him in a job following the club’s failure to qualify for the Champions League.
Instead United, who lost Marcus Rashford and Marcos Rojo to injury and Chris Smalling to an extra-time red card, will go into the Europa League, along with West Ham United, after United’s Wembley win freed up an additional qualifying berth.
Palace manager Alan Pardew, meanwhile, met with FA Cup heartbreak for the third time, having been on the losing side against United with the south London club in 1990 and overseen West Ham’s defeat on penalties by Liverpool in 2006.
“The players have given me everything,” Pardew said.
“We played with heart and passion. It was a great cup final. Manchester United did the same. It made for an enthralling tie and a game that could have gone either way.”
United enjoyed the best of the first half, but Pardew was infuriated when referee Mark Clattenburg brought play back for a free-kick despite Connor Wickham jumping to his feet and racing into the box after being dragged to the turf by Smalling, who was booked.
United’s control was even more pronounced after half-time as Van Gaal’s men succeeded in pinning Palace back and they hit the woodwork twice in the space of eight minutes through Marouane Fellaini’s drilled shot and Anthony Martial’s header.
Injuries then deprived United of Rojo and Rashford, with Matteo Darmian and Ashley Young coming on, while Puncheon replaced Yohan Cabaye.
The Palace substitute made an immediate impact. His 78th-minute corner from the left was headed away by Fellaini, but Joel Ward helped the ball back into the box and Puncheon brought it down before blasting a vicious left-foot shot past David de Gea at his near post.
Pardew celebrated with a touchline dance, but within three minutes Palace’s lead had vanished.
Rolling back the years, Rooney did superbly to reach the byline on the right before digging out a cross that was chested down at the back post by Fellaini for Mata to strike a volley that rattled between Ward’s feet and crept over the line.
United lost Smalling when the England centre-back received a second yellow card for hauling Yannick Bolasie back by his ankle as he lay on the turf.
The teams exchanged chances in the second extra period -- De Gea thwarting substitute Dwight Gayle with his feet, Carrick heading wide -- before United academy graduate Lingard, a 90th-minute replacement for Mata, claimed a piece of FA Cup history.
Antonio Valencia’s drilled cross was cleared by Damien Delaney, but the ball popped up for Lingard, who sent a volley whistling into the top-left corner before tearing off his shirt and racing towards the United end in gleeful celebration.
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