The Spaniard shot a final-round 66 at the Real Club Valderrama to make up seven strokes on overnight leader Lahiri and finish in a tie on five under.
A short par putt at the second hole of the sudden-death play-off was enough to secure Garcia his first LIV win and prize money of £3.15m.
“Without a doubt [one of the highlights of my career],” Garcia said.
He spoke about it being a big Sunday for Spanish sport, saying: “Not only that, but also Carlos winning. Alcaraz won today [at Wimbledon].
“Hopefully Spain wins tonight. It would be an unbelievable weekend. But I played well, played well in the play-off. It’s just a tough hole. But so happy.”
Spain’s victory against England in the Euro 2024 football final duly came, providing more delight for Garcia and making it a remarkable day of achievement for the country.
Garcia’s most recent victory had come at the 2020 Sanderson Farms Championship.
England’s Tyrrell Hatton finished third, a shot back from the leaders on four under, with American Patrick Reed and South Africa’s Louis Oosthuizen tied for fourth on three under.
“I felt pretty gutted for Lahiri,” Hatton said. “It was a bit awkward on the 18th green with the crowd because they wanted Sergio to win.
“I think everyone thought it would be done there, and unfortunately for Lahiri, they ended up having to go into a play-off.
“From my point of view, nice to have another good week going into the Open.”