An absorbing Wembley showpiece had somehow ended 0-0 after extra time despite a raft of chances and near misses for both sides with fine performances from the two goalkeepers.
Substitute Kostas Tsimikas slotted the winning penalty after Chelsea captain Cesar Azpilicueta’s had hit the post and Alisson had saved Mason Mount’s effort.
It was a carbon copy of the League Cup final in February, which Liverpool won 11-10 on penalties after that game also finished goalless.
“I’m really proud of my boys,” Liverpool manager Klopp said. “We are mentality monsters but there were mentality monsters in Chelsea colours as well — it was one penalty.
“Chelsea played outstanding but in the end there must be one winner and that was us today.”
Saturday’s win means Liverpool have won 50% of their target for the season.
They are three points behind Manchester City in the Premier League race with two games to go and meet Real Madrid in the Champions League final on May 28.
“This is something that will give us even more confidence to keep on going in the Premier League and also for the Champions League final,” Alisson, who made a crucial save from Marcos Alonso in the first half, said.
Liverpool had the best of a pulsating first half with Luis Diaz close several times, before Chelsea came back in the second, with Alonso rattling the crossbar.
Klopp’s Liverpool enjoyed the greater possession and finished the 90 minutes on top, Diaz and Andrew Robertson both hitting the post in the final 10 minutes and the indefatigable Diaz whistling a shot just wide in the 90th.
Tired legs on a warm day contributed to a rather anticlimactic extra time with both sides appearing to have decided to take their chances in a shootout.
Sadly for Chelsea, as in February, it was a case of so near yet so far although manager Thomas Tuchel had no regrets.
“Like in the last final, the League Cup, no regrets. I told the team I was proud,” he told reporters. “We played 240 minutes in two finals against maybe the most dangerous attacking team in the world and it’s 0-0.”
“I was sure during the match the momentum was on our side but unfortunately I was not right.”
The only blot on another memorable day for Liverpool was striker Mohamed Salah being withdrawn in the first half with an injury.
Liverpool captain Jordan Henderson was handed the Cup by Prince William to roars from the Liverpool fans while the Chelsea end had largely emptied.
“It’s a big moment for us, we haven’t been in this final for some time so to win it was special,” Henderson said.
The win was Liverpool’s eighth in the 150-year history of the FA Cup, drawing them level with Chelsea and Tottenham Hotspur. Arsenal have won the most with 14.