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.
