Frank Lampard’s side will face London rivals Arsenal in the final on August 1 thanks to another nightmare display in a horrendous season for De Gea.
The Spaniard was at fault when he let Olivier Giroud’s shot trickle over the line late in the first half at Wembley.
And De Gea made an even worse mistake moments after the interval when he allowed Mason Mount’s shot to evade his weak attempted save.
While the spotlight was on De Gea and his future at the club after his latest howlers, Chelsea were by far the better team as they reached the FA Cup final for the first time since they last lifted the trophy in 2018.
Harry Maguire’s own goal was a fitting end to a woeful performance from United, who lost for the first time in 20 games in all competitions despite Bruno Fernandes’ late penalty.
United had beaten Chelsea three times this season, with two wins in the Premier League and one in the League Cup.
But Lampard, who won the FA Cup four times as a player, had the last laugh with a result that moves him closer to silverware in his first season as Chelsea boss.
United manager Ole Gunnar Solskjaer had complained about Chelsea having two days more rest than his team before the semi-final, but his gamble of starting Paul Pogba, Anthony Martial and Mason Greenwood on the bench backfired badly.
United looked out of sync after switching to a back three formation and it was Chelsea who set the tempo despite the absence of injured winger Christian Pulisic.
Foreshadowing the errors to come, Reece James’ long-range blast forced De Gea into an awkward early save.
Dominating possession and pressing with intensity, Chelsea should have been ahead when Marcos Alonso headed over after Cesar Azpilicueta’s cross found him in a good position at the far post.
Fernandes was subjected to some crunching tackles as Chelsea tried to knock United’s influential playmaker out of his rhythm.
– Comedy of errors –
When Eric Bailly was badly injured after a clash of heads with Maguire late in the first half, Solskjaer ditched his malfunctioning formation and sent on Martial in a return to their usual game-plan.
Martial nearly had an immediate impact after the lengthy injury delay as Kurt Zouma’s challenge on him sparked a penalty appeal that was rejected by VAR.
But it was Chelsea who took the lead deep into first half stoppage-time with Giroud’s fourth goal in his last five games.
Anticipating Azpilicueta’s low cross perfectly, Giroud made an astute run in front of Victor Lindelof and flicked his close-range shot past the slow to react De Gea with the outside of his foot.
If that was bad from De Gea, there was even worse to come one minute after half-time.
It was a comedy of errors from United as Brandon Williams gifted possession to Mount in midfield.
Advancing unchecked by United’s back-pedalling defence, Mount hit a long-range drive that lacked power and should have saved by De Gea, but instead it squirmed through his grasp into the net.
Pogba and Greenwood were introduced by Solskjaer, but Chelsea remained on top and De Gea finally made a decent save as he kept out Giroud’s flick from Alonso’s cross.
Chelsea put the result beyond doubt in the 74th minute when Mount found Alonso and Maguire turned the Spaniard’s cross into his own net under pressure from Antonio Rudiger.
Once again De Gea didn’t react quickly enough and it would be no surprise if Dean Henderson, currently on loan at Sheffield United, is competing for the Spaniard’s place next term.
It was no consolation for United when Fernandes scored from the spot in the 85th minute after Callum Hudson-Odoi tripped Martial.