The Belgian forward successfully converted from the spot a quarter of the way into the 137th final for what proved to be the game's only goal, punishing Phil Jones for his last-ditch challenge inside the box.
United improved in an attacking sense in the second half, coming particularly close through a late headed chance for Paul Pogba, but they could not find a way through.
The big news ahead of the match was the absence of Romelu Lukaku from Mourinho's starting lineup, only being deemed fit enough for a place on the bench following his ankle injury layoff, while Conte used Tiemoue Bakayoko in a five-man midfield at the expense of Willian.
Chelsea looked the more threatening side on the rare occasions that they committed players forward, creating the first opening of the match 10 minutes in through matchwinner Hazard.
The Belgian forward had space to run into on the counter and attempted to catch out David de Gea, who read the danger and stuck out a big leg at his front post.
In what was a tight first half, things threatened to open up slightly midway through when Bakayoko was sent to the floor by Nemanja Matic at one end and Alexis Sanchez under contact from Victor Moses at the other.
Neither incident warranted a penalty, however, with referee Michael Oliver - who had VAR there to use it should he wish - getting both decisions correct.
Oliver was also justified when pointing to the spot 20 minutes in after Hazard used his first touch from Cesc Fabregas's ball over the top to charge towards the opposition box, seeing his run halted by Jones once caught out of position and then unable to redeem himself with a lunging tackle.
Hazard sent De Gea the wrong way from the spot for the game's decisive moment - just the second time United had shipped a goal in this season's competition.
Not for the first time this season, United's lack of risk-taking was proving to be a problem, failing to test opposition keeper Thibaut Courtois - in for his first FA Cup appearance of the campaign - at any point in the opening 45 minutes.
Pogba dragged an effort wide and Marcus Rashford failed to find the target from his only sight of goal right on the brink of half time.
United took that momentum into the second half, pushing the Blues back and finally registering a serious attempt just short of the hour mark when Rashford's shot from range was parried by Courtois.
Sanchez thought that he had netted his ninth Wembley goal in the same number of outings soon after, only for the offside flag to correctly rule out his close-range finish after Courtois brilliantly kept out Jones's initial header, VAR being used to confirm the correct call had once again been made.
VAR was required for a second time with a quarter of the game left, adjudging that Ashley Young did not deliberately use his arm to block Moses's cross into the box.
That came immediately after Marcos Alonso squandered a glorious chance, refusing to hit N'Golo Kante's pass first time and instead taking it with his right, allowing De Gea to steady himself an make the save.
Rashford was then played through by Jesse Lingard as the match opened up, unable to lift the ball over Courtois who produced another good stop.
Mourinho turned to Lukaku and Anthony Martial with 17 minutes to play at a point in the game when his side were looking their most threatening.
A Matic drive from 25 yards was parried by Courtois and, two minutes later, Pogba met a corner completely unmarked from a central position, glancing it wide of the far post.
That would prove to be the last chance for United to salvage extra time in their record-equalling 20th final, with Chelsea seeing things through to lift the FA Cup for an eighth time.
CHELSEA (3-5-1-1): Courtois; Azpilicueta, Cahill, Rudiger; Moses, Kante, Fabregas, Bakayoko, Alonso; Hazard (Willian 91'); Giroud (Morata 89')
MANCHESTER UNITED (4-3-3): De Gea; Valencia, Jones (Mata 87'), Smalling, Young; Matic, Herrera, Pogba; Lingard (Martial 73'), Rashford (Lukaku 73'), Sanchez