Falcao swooped for his 17th goal of the competition just before half-time, timing his run to perfection to meet compatriot Fredy Guarin's precise cross and brilliantly direct a header past Braga keeper Artur.
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Braga, the competition's surprise packages who knocked out former European champions Liverpool and Benfica, should have equalised when Mossoro went clean through seconds after half-time, only to shoot straight at the goalkeeper.
However, they did not have enough attacking guile to stop Porto boss Andre Villas Boas emulating the club's greatest coach Jose Mourinho by winning this competition and the domestic league in his first season in charge. He also became the youngest coach to win a European trophy.
"Without a doubt this is a great feat. We have one trophy left for a memorable season," Villas Boas said.
"This has a huge emotional impact for us. Round after round, we kept believing more. Porto becomes an even more special club, even more unique. It adds another trophy, which is important and builds its future."
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."
LAST CHANCE
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 Jurgen Klinsmann.
It also succeeded in shaking the game into life and Braga would have been level h
