Sergio Conceicao's men were fortunate, but Aderlan Santos' 30th-minute goal was enough to give them victory at the Estadio do Restelo on Saturday.
Santos' goal on the half-hour mark saw Braga move back within six points of league leaders Benfica.
But Benfica, Porto and third-placed Vitoria Guimaraes are all playing on Sunday.
After Santos' opener, hosts Belenenses missed a 65th-minute penalty through Fredy and they were unable to find a way back into the contest.
The win extended Braga's unbeaten run to eight matches in all competitions.
At the other end of the table, bottom side Gil Vicente remain winless in the league after a 1-1 draw at home to Academica.
Penafiel made it back-to-back wins, climbing out of the relegation zone with a 2-1 victory over Nacional.
Elsewhere, Cicero's 90th-minute winner saw Pacos de Ferreira edge Arouca 2-1, ending a three-match winless run in the league and moving them up to sixth.
