In the first-half stoppage time, Olivier Giroud opened the scoring for the Blues, after Eric Bailly's head injury, required extra minutes.
César Azilicueta's cross was intercepted by the Frenchman to avoid a flapping David De Gea.
De Gea struggled to cover himself in glory again immediately after the break when he failed to hold Mason Mounts out of the penalty box.
a low Marcos Alonso centre, Harry Maguire poked into his own goal to
settle the game, while Bruno Fernandes scored late from the penalty
The Blues must challenge Arsenal in a repeat of the 2002 and 2017 finals on August 1, back at Wembley.
Here are 5 talking points from Wembley...
1. Arsenal vs Chelsea
Between them, they have 14 appearances at one of the Old Wembley, Millenium Stadium or New Wembley in the past 20 years.
They have met each other twice - Arsenal winning in both meetings in 2002 and 2017.
Tim Lovejoy will tell you about Ray Parlour in the former!
The Gunners might have the advantage in FA Cup finals, but not in recent finals
The Blues were utterly rampant in the Europa League final last year - Arsenal will want revenge.
It all adds up to be an exciting showpiece between two exciting young managers and schizophrenic squads.
Pity, it will be behind closed doors.
2. Formation ch-ch-changes
Like Mikel Arteta, the duo both decided to go with a back five - one scared of the prospect of Martial, Rashford and Greenwood, the other Willian, Giroud and Pulisic.
Neither of those fully formed front threes materialised on the team sheet.
Perhaps both went slightly too conservative, as that is how it felt for much of the first half as neither team seemed overly keen on piling on the pressure in the final third.
Solskjaer had used this system in United's victory at Stamford Bridge in February, it worked to a tee then, and however dull much of the first half was to watch, Chelsea didn't look like scoring here.
Bailly's sickening head injury forced Solskjaer to rethink and readjust and the decision to return to a more conventional 4-3-3 appeared to be their downfall - along with David De Gea's flapping.
And on that note...
3. De Gea's flapping
Within 50 minutes, David De Gea had shipped double that number.
It begs the question of why the Argentine was forced down to the bench, especially as other positions saw the Premier League regulars rested - see Martial, Greenwood and Paul Pogba on the bench.
On the other hand, De Gea is becoming more and more of a liability.
"The most overrated keeper I have seen in a long long time," Roy Keane memorably ranted after his Tottenham mistake.
His decline has been fairly steady over the past couple of seasons, and while he can still produce some other-worldly saves, the gaffes are high profiled.
The way he let Giroud's shot past him in the first half looked ungainly, and he ultimately should have done better, for Mount's doubler he should have saved it in his sleep.
There may well have been a bit of power in the strike, but the Spaniard allowed the body to slither under him.
There is some irony that De Gea's downfall has coincided with United getting stronger elsewhere on the pitch, after the Premier League winner carried the club for a number of years.
But with Dean Henderson returning this summer from his exemplary loan stint at Sheffield United, his days may be numbered.
4. Blues give tough stuff to Fernandes
But it was a difficult welcome to Wembley for the Portuguese playmaker as Chelsea ensured his first ride at the famous old ground was anything but comfortable.
Throughout the first period, United’s No.18 wasn’t allowed to settle by Chelsea’s midfield - notably Mateo Kovacic.
The Croatian and Jorginho were both regularly snapping at the heels of Fernandes, who came in for some rough treatment - being fouled three times in quick succession during one spell.
Chelsea gave him no quarter - through both fair means and foul - forcing him to move deeper and deeper to find possession, into areas where he was more easily controlled by Lampard’s side.
Taking his penalty was a rare moment of respite from the constant attention.
5. Giroud vs Abraham
But since the restart has Giroud proven his place as the Blues' most trusted striker?
Abraham has had a high-class first season as a Premier League regular, with 17 strikes for club and country.
However, Giroud just has the knack, especially in the FA Cup.
He may not run about as Abraham does, but sometimes simply standing still can cause a nuisance in itself.
The Frenchman has five goals in eight appearances since football returned in June, Abraham - in admittedly less game time - has one.
Now he has the chance of a fifth FA Cup winner's medal and hurt his former employers.