Jurgen Klopp's side repeated their Carabao Cup final victory in February, the decisive moment coming when Liverpool goalkeeper Alisson saved Mason Mount's spot-kick, leaving Kostas Tsimikas to secure Liverpool's second trophy of the season.
The Reds are still in the Premier League title race and have the Champions League final to come against Real Madrid.
Liverpool had the better of an eventful final, with the outstanding Luis Diaz and Andrew Robertson hitting the woodwork, although it may come at a price with Mohamed Salah going off injured in the first half and Virgil van Dijk going off after 90 minutes.
It is a devastating blow for Chelsea and manager Thomas Tuchel to lose in this manner yet again as they had chances - with Marcos Alonso hitting the post and also being denied by Alisson - but become the first side to lose three successive FA Cup finals.
When Edouard Mendy saved Senegal team-mate Sadio Mane's penalty in the shootout, when the Liverpool forward only needed to score to win the FA Cup, it just seemed for one moment that the Reds' assault on four trophies might just be interrupted.
Alisson put Liverpool back on course when he saved from Mount, who was inconsolable as Tsimikas sent the Liverpool fans wild by converting the final penalty.
Once again Liverpool had prevailed against fiercely disciplined and determined opponents, even though they lost Salah to what looked like a muscle injury before half-time and Van Dijk did not emerge for extra time.
It remains to be seen how serious those problems are but at present it looks like Liverpool can overcome most obstacles put in front of them, even though it once again took penalties to claim their first FA Cup since 2006.
Diaz was the game's outstanding player, running Chelsea ragged and peppering Mendy's goal with efforts until he was substituted, exhausted, to a standing ovation.
Klopp refers to his players as "mentality monsters" and this illustrates why. Players from both sides gave so much that they were almost out on their feet at the final whistle.
Manchester City remain favourites in the Premier League, three points ahead and with a superior goal difference, and this was a strength-sapping occasion that will have taken much out of Liverpool before they face Southampton at St Mary's on Tuesday.
What we do know, though, is that Liverpool possess remarkable powers of resilience and recovery as they continue their march on history.
For the second time this season, Liverpool got the better of Chelsea in a penalty shootout to add the FA Cup trophy to the Carabao Cup they had already gotten their hands on, keeping their quadruple dreams alive.
As the Carabao Cup final had, Saturday's FA Cup final ended goalless after 90 and then 120 minutes, but Chelsea missed two of their seven penalties, with Konstantinos Tsimikas then netting the winner with the 14th of the shootout.
Liverpool were on top early on and were the only team in the contest during the opening exchanges. Luis Diaz, in particular, was excellent from the off and he had the game's first chance, while he was heavily involved in almost everything dangerous that happened in the initial 90 minutes.
Chelsea had a handful of chances fall Christian Pulisic's way, but the American was unable to capitalise.
Thomas Tuchel's side would have been somewhat relieved when Mohamed Salah was forced off injured after just half an hour.
After the break, it was a mystery as to how the game remained goalless. Both sides missed their fair share, and the scores could well have been level at 2-2 or even 3-3.
Luis Diaz struck the post inside the final 10 minutes, and then Andy Robertson did the same though the Scot perhaps should have scored from the position he found himself in after James Milner's cross.
In the shootout, the first two were converted before Cesar Azpilicueta missed Chelsea's second and the game's third penalty.
Edouard Mendy made amends for the Spaniard's miss by denying Sadio Mane as he had the chance to win it.
Alisson Becker then stopped Mason Mount's effort with Chelsea's seventh, and Tsimikas converted past Mendy for the winner.
Liverpool's attention now turns to a Southampton on Tuesday night, with their chances of a quadruple still alive. They also have Real Madrid to face in the Champions League final this season.
Liverpool have won 49 majors trophies including 19 Premier League titles, seven FA Cups, nine Carabao Cups, six Champions League trophies, three UEFA Cups, four European Super Cups and one Club World Cup.
Jurgen Klopp has celebrated five of those 49 trophies and should Liverpool beat Chelsea on Saturday at Wembley, he will win his first FA Cup with the Reds.
It took a penalty shootout for Liverpool to beat Chelsea to win the FA Cup at Wembley on Saturday, as the Reds' chances of a quadruple live on for the time being.
Having beaten the Blues in another shootout to win the Carabao Cup in February, Liverpool now have eyes on the Premier League title and the Champions League, with the club set to face Real Madrid in the final in Paris at the end of May.
While many in recent years have played down the importance of the FA Cup, Liverpool and Jurgen Klopp were undeniably delighted to have got their hands on yet more silverware on Saturday.
As well as it being another trophy for their sizeable cabinet, the FA Cup win also brings prize money into the club.