United fell behind to substitute Jason Puncheon's 78th-minute strike, but Juan Mata levelled within 180 seconds to take the game to extra time.
Chris Smalling – earlier embroiled in controversy after hauling back a goal-bound Connor Wickham – saw red just before the end of the first additional 15 minutes after a foul on Yannick Bolasie, but substitute Lingard proved the Reds hero as they etched their name on the famous trophy for a record-equalling 12th time and first since 2004, casting aside pre-match speculation that Louis van Gaal is to be replaced by Jose Mourinho.
The Dutchman's failure to steer United into the UEFA Champions League is a key catalyst for his likely exit, but the 64 year-old can at least boast a major honour from his two-year tenure after Sunday's deserved victory.
However, it was heartbreak for Palace and their boss Alan Pardew, who played when the club last reached the Cup final – United prevailing back in 1990 after a replay – and managed West Ham in their 2006 penalty shootout loss to Liverpool.
Palace were on course for a shock victory after local hero and substitute Jason Puncheon fired them ahead with just 12 minutes remaining but Wayne Rooney set up an immediate Juan Mata equaliser.
United lost defender Chris Smalling in extra time after he hauled back Yannick Bolasie to incur a second booking but United snatched victory with a fine volley from substitute Lingard after 110 minutes.
Defeat was harsh on valiant Palace, who were frustrated by a series of decisions by referee Mark Clattenburg in the first half and fought to the end.
A touchline dance from Alan Pardew after Puncheon struck suggested they sensed history and revenge for defeat in the 1990 final, but their jubilation was shortlived.
United could argue, after hitting the post twice and bossing large spells, they deserved victory and a first trophy since the retirement of Sir Alex Ferguson.
