The German got the job done at the second extra hole, making a two-putt birdie at the par-five 18th as Harrington could only manage a par after a fluffed chip shot.
Harrington, who has now finished runner-up in both his Senior Open appearances, had missed an eagle putt to win on the 72nd hole, before both players made birdies on the first play-off hole.
Extra holes were required after the pair finished the tournament on five over par, with nobody able to break par for the second day running as the field faced howling winds and rain in Wales.
It is the highest winning score at Europe’s only Senior Major Championship since Bob Charles finished on seven over at Royal Lytham & St Annes in 1993.
Cejka emulates four-time champion Bernhard Langer as just the second German to win the Senior Open as he adds the trophy to his wins at the Regions Tradition and KitchenAid Senior PGA Championship in 2021.
“I can’t believe I’m standing with the trophy here,” Cejka said.
“Seeing all those great names on the trophy, coming in here with all the pictures and everything, all the guys who won it before me, now holding it myself, it’s surreal.”
Harrington was bidding to become just the fifth player after Charles, Gary Player, Tom Watson and Darren Clarke to win both The Open and Senior Open.
“I hit a tentative putt on the 72nd hole,” he reflected. “You’ve got a chance to win the tournament.
“I was trying to not hit a bad putt and I should have been trying to hit a great putt.”
There were 18 players within four shots of overnight leader Cejka as the final groups teed off.
Despite a lost ball on the first hole resulting in a double bogey, Cejka had doubled his overnight one-shot overnight when he hit the turn but a bogey at the tenth saw that halved.
Cejka and Harrington both made birdies at the par-three 12th, before a succession of gutsy pars by the German helped him open up a two-shot lead with three holes to play.
As others in the groups ahead began to drop out of contention, Harrington missed a five-footer for par at the 16th to draw closer as both members of the final group made a bogey.
Another dropped shot was to follow for Cejka after he failed to find the 17th green in two, before Harrington set up an opportunity to win his second Senior Major in grandstand fashion on the final green in regulation play.
Harrington was again close to sealing victory at the first play-off hole as his eagle putt from off the back of the green agonisingly missed to the left, before Cejka extended the contest.
After finding the fairway with his drive when the players returned for the second play-off hole, Cejka found the putting surface with his second shot while Harrington went through the green before his error with a wedge that ultimately proved decisive.
Vijay Singh finished in third place at seven under, a shot clear of Michael Jonzon.
The Fijian started the day one shot adrift of Cejka but signed for a 77 as he made a birdie at the last, while Sweden’s Jonzon finished with a 75.
Phillip Archer, making his Senior Open debut, finished in a tie for fifth at nine over, alongside 2002 Ryder Cup winner Phillip Price.
Y.E. Yang, the 2009 US PGA champion, climbed 44 places to finish in a share of 11th after a level par 71, the joint best of the day.
John Kemp finished as the leading amateur in a tie for 14th on 12 over after an impressive closing 74.
