The French teenager fired in an injury-time winner in a 2-1 win over Everton at Wembley on Saturday.
After Marouane Fellaini’s first-half strike for United against his former club was cancelled out by Chris Smalling’s 75th-minute own goal, Martial struck three minutes into stoppage time.
United’s opponents in what will be a record-equalling 19th FA Cup final will be Crystal Palace who beat Watford 2-1 last night.
David de Gea was as much the United hero as Martial, the Spain goalkeeper keeping out Romelu Lukaku’s 57th-minute penalty after Timothy Fosu-Mensah had brought down Ross Barkley.
De Gea says: “Everton played really well and had some chances.
“In one second Anthony Martial scores a goal and you win it in the last minute, it’s unbelievable.”
In a rollercoaster of a semifinal, with a string of missed chances keeping both sets of fans on a knife edge, United had a penalty appeal rejected in the 66th minute when Fellaini’s shot was blocked by Phil Jagielka’s arm.
United boss Louis van Gaal has had all too few moments of such unbridled enjoyment in his time.
But he adds: “When you see the joy in the eyes of the players it is fantastic to see but also for the fans.
“We deserved to go to the final. I think the referee... we didn’t have any fouls in our benefit. He changed the match I think.”