They salvaged a point when striker Oscar Cardozo struck in the 73rd minute with a penalty but Benfica failed to find a winner at the end of an electrifying second half at a packed Luz stadium after a tame first 45 minutes.
Benfica's Argentina winger Eduardo Salvio, signed from Atletico Madrid in the close season, had put the hosts ahead from close range just after the break.
The crowd was still celebrating the breakthrough when 21-year-old Melgarejo, an adapted left back, left them dumbstruck five minutes later as he sent a flying header into his own net while trying to clear a swerving cross.
His official debut went from bad to worse when a clumsy clearance in the box fell to Braga's Brazilian midfielder Alan who set up compatriot Mossoro for an easy goal as the visitors grabbed the lead just past the hour mark.
However, Braga were dealt a severe blow in the 71st minute when Benfica were awarded a penalty and Cardozo converted after defender Douglao was dismissed for a second yellow card for handball although Custodio appeared to be the culprit.