Marouane Fellaini gave Louis van Gaal's side the advantage in the 34th minute after an uninspiring first-half display from the Blues, but they were a team transformed in the second-half.
David de Gea saved Romelu Lukaku's penalty, but the Toffees equalised in the 75th minute through Chris Smalling's own goal. After a valiant effort in the second-half, Martial's injury-time winner ended Everton's FA Cup dreams.
Early chances for Lukaku
The match could have run a different course had Romelu Lukaku taken his pair of chances in an open start to the semi-final, with chances for either side to claim an early advantage, but the Belgian's touch evaded him at crucial moments.
Lukaku's best chance of the first-half came within the first five minutes of the match as the Toffees looked to hit Manchester United on the counter-attack and use the Lukaku's pace and strength. The striker had a glorious chance to give Everton the advantage in the fourth minute; using his strength and power to win the ball before chesting the ball past Daley Blind to find himself clear. However, a heavy touch while rounding David de Gea took him away from goal and Wayne Rooney was there on the goal line to deny Everton an early lead.
The Belgian found himself behind the United defence again in the 17th minute, albeit from a difficult angle, but Lukaku did not hit his shot cleanly and it was an easy enough save for De Gea.
Former Blue gives United the lead at the break
Manchester United were dominant in the first-half with around two thirds of possession and found it far too easy to play through the Blues. The Red Devils' first opening of many in the first-half fell the way of Jesse Lingard, whose first-time attempt at the end of a sweeping Rooney pass produced a good reaction save from Joel Robles. Wayne Rooney and Anthony Martial were the next Manchester United players to test the Everton goalkeeper, before United did eventually make a derserved breakthrough in the 34th minute.
Former Toffee Marauone Fellaini fired home from close-range when picked out by Martial. The Frenchman burst into the box, getting the better of stand-in right-back Muhamed Besic to find his teammate in a central position. Fellaini made no mistake in powering the ball past Robles. That proved to be the end of the first-half chances and the half-time whistle was greeted by boos from Everton's support in Wembley.
Lukaku denied from the penalty spot, before Smalling's own goal draws Toffees level
Everton started the second-half far better than the first and the Toffees were given a great chance to equalise after referee Anthony Taylor pointed to the spot after Timothy Fosu-Mensah brought down Ross Barkley in the area. Romelu Lukaku stepped up but De Gea produced a brilliant save to his right to deny Lukaku for a third time.
The miss did not seem to dishearten Everton, if anything it spurred the Toffees on to press and fight for an equaliser. Tom Cleverley fired over from Aaron Lennon's cross, before turning provider for Lukaku, but the striker headed over.
Jagielka denied Fellaini in the 66th minute with a desperate lunge, but replays showed that the Everton captain used his hand when diving in to stop the ball rolling across the line. However, Everton's pressure was rewarded in the 76th minutes courtesy of a Manchester United player. Chris Smalling turned Gerard Deulofeu's teasing cross beyond De Dea and into his own goal to set-up a frantic and an end-to-end final 15 minutes.
A frantic final 10 minutes ends in despair for the Blues
Everton came close to leading three times in the space of a few minutes. First De Gea could only push Deulofeu's shot into the centre of his box, somehow evading the prowling Lukaku. The striker then headed wide moments later, before his shot was superbly blocked by his international teammate Fellaini.
However, a vailaint second-half display for the Toffees ended in despair as the match looked destined to be decided in either extra-time or by a penalty shootout. The ball was played through for Martial, who showed great composure to slot the ball beyond Joel and into the bottom corner to send United to an FA Cup final for the first time in 12 years.