Chelsea haven't won a domestic trophy since lifting the FA Cup in 2018 and their wait will go on for another season after they blew the lead at the Amex Stadium.
Enzo Maresca's side were gifted the lead in the fifth minute when Brighton goalkeeper Bart Verbruggen fumbled Cole Palmer's cross into his own net.
It was a horrendous mistake but Chelsea failed to press home their advantage.
Thrashed 7-0 at Nottingham Forest in the Premier League last weekend, Brighton bounced back impressively from the second worst defeat in the club's 123-year history.
They equalised in the 12th minute as Joel Veltman's cross reached Georginio Rutter, who found space between Chelsea defenders Trevoh Chalobah and Tosin Adarabioyo to flick a header into the far corner.
And Brighton completed their fightback in the 57th minute when Mitoma clipped a deft finish past Chelsea's Robert Sanchez despite the visitors' claim for handball.
