Porto cruised to the Portuguese title undefeated and reached this final by knocking out the likes of Spain's Sevilla and Villarreal.
Their opponents, playing in their first European final, created the first chance when midfielder Custodio fired a half volley wide of Porto captain Helton's goal on four minutes.
Braga coach Domingos was almost certainly taking charge of his team for the last time with media speculation strongly linking him with a move to Sporting.
"I am very proud, I lived unique moments here. These players also did, it's a beautiful story," he said.
"May Braga continue to grow, we dignified Portuguese football."
Porto had the better of the first half and burly Brazilian forward Hulk cut in from the wing and zig-zagged past two defenders before flashing the ball across the Braga goal.
Hulk continued to prove a menace and was forcibly stopped in his tracks twice at the cost of two yellow cards in quick succession.
But it was his strike partner Falcao who broke the deadlock a minute before the break, handing the game the jolt it needed with his 38th goal of the season and his team's 137th.
The goal meant the prolific striker, who scored five goals in the semi-final against Villarreal, took his record-breaking tally for a single European competition further past the previous mark of 15 held by Juergen Klinsmann.
-Porto's Falcao celebrates after scoring against Braga during their Europa League final soccer match in Dublin
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