Brighton keeper Bart Verbruggen gifted Chelsea a fifth-minute lead when he bundled a Cole Palmer cross into his own net.
The hosts were not behind for long, however, as Georginio Rutter equalised seven minutes later with a glancing header.
Brighton were the better side after the break and Japanese winger Mitoma sealed the tie in the 57th minute with a neat flicked finish over Chelsea goalkeeper Robert Sanchez.
Defeat means Chelsea have not won away in any competition since early December and their only realistic chance of silverware in manager Enzo Maresca's first season at the helm is in the UEFA Conference League.
Brighton have been inconsistent in the league under their 31-year-old manager Fabian Hurzeler but they provided a great response to last week's 7-0 drubbing by Nottingham Forest, especially after such a calamitous start.
"It's good that everyone rallied around and showed their fighting spirit," Brighton winger Tariq Lamptey said.
"We showed that we are together and we turned it around."
Things looked bad for the hosts when Palmer volleyed a cross towards goal and Verbruggen spilled the ball into his goal.
Rutter spared his blushes soon after though as Joel Veltman's cross from the right evaded two Chelsea defenders and the Frenchman guided his header beyond Sanchez.
There was a hint of controversy about Brighton's winner with a suspicion of handball in the build-up before Mitoma showed a cool head to lift his finish over Sanchez.