Pompey made just one change from the side which drew 0-0 with Aston Villa last weekend, with Glen Johnson missing out due to a groin injury and Hermann Hreidarsson returning to the starting eleven.
The home side made the brighter start and the Portuguese outfit broke the deadlock with eight minutes played in the Municipal Stadium.
Papa Bouba Diop conceded a free-kick fully 30 yards out and Uruguayan forward Luis Aguiar curled home a superb effort to leave England goalkeeper David James stranded.
James then blocked an effort from Vandinho as Braga began to turn the screw, before Peter Crouch placed an effort wide of the target.
The striker then forced Eduardo into a smart save as Pompey started to find their feet, before the home keeper was drawn into further action twice in quick succession by Jermain Defoe.
There were no more clear chances for either side up to half-time, with Braga maintaining their narrow advantage.
Pompey brought on Nadir Belhadj at the interval, but the home side doubled their lead in the first minute of the second half, as Wason Renteria turned his marker in the area and fired a low shot past James.
Aguiar went close just before the hour mark as Braga started to dominate, before Harry Redknapp brought on striker Nwankwo Kanu to try and change things around.
Sub Cesar Peixoto tested James from a free-kick and Aguiar placed an effort wide of target as Braga came closest to the third goal of the game.
Diop fired a 25-yard effort over the top as Pompey tried to find a way back into the game, before Defoe was foiled by Eduardo again.
Three minutes from time Portsmouth's misery was complete as Alan converted from close range after an initial shot had come back off a post.