Valencia's Yunus Musah blazed over in the shoot-out, allowing Juan Miranda the chance to score the winning penalty at La Cartuja as Betis claimed their fourth major trophy in the club's 115-year history.
Borja Iglesias had headed Betis in front but Hugo Duro equalised for Valencia before half-time and neither side could find a winner, either in the second period or extra time.
But Musah's error and Miranda's cool head gave Betis the cup for a third time, following the club's two previous triumphs in 1977 and 2005.
Joaquin, the 40-year-old winger, who made his debut for Betis aged 19 in 2000 and played in the final 17 years ago, came on in the 86th minute and scored a penalty. It remains to be seen whether Joaquin decides this is a fitting end now to what has been a remarkable career.