Radamel Falcao provided the winner in the 44th minute, meeting a perfect cross from the right by Fred Guarin to head into the top left corner of the net after a largely tentative first half.
Substitute Mossoro nearly responded just a minute after the break but had his low shot saved by Helton when free with the goalkeeper, wasting what proved to be Braga's best chance for an equalizer.
It is Portuguese champion Porto's first European title since winning the 2004 Champions League under Jose Mourinho and comes after a season when it went undefeated in the domestic league.
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