Veteran striker Marco Di Vaio was the hero for the MLS side, with the Italian's 21st-minute goal enough to sink the El Salvadorians in their heated Group Three opener.
After being denied by goalkeeper Luis Contreras on numerous occasions in the opening stages, 38-year-old Di Vaio popped up to make the breakthrough, finding himself unmarked inside the area before heading home Felipe's floated cross.
Montreal - in the midst of a six-game losing streak in MLS to sit adrift at the foot of the Eastern Conference standings - ended the match with 10 men following Hassoun Camara's dismissal in the 72nd minute.
Camara saw red for a late challenge on FAS midfielder Raul Renderos, while Impact coach Frank Klopas was also sent to the stands 10 minutes later for criticising referee Hugo Cruz.
Despite the numerical advantage, FAS - one game into their Primera Division campaign - could not find an equaliser.
Leon and Olimpia were the other winners on the opening matchday.
Second-half substitute Jose Cardenas netted a brace as Liga MX club Leon routed Isidro Metapan 4-1 in El Salvador.
Visiting Leon were leading 2-1 at half-time courtesy of strikes from Derley and Luis Franco before the 15-minute mark, while Hector Ramos was on target for Isidro Metapan during that period.
But the introduction of Cardenas - on loan from America - just past the hour-mark paid immediate dividends, as the attacker scored twice in the space of 12 minutes to secure maximum points in Group Seven.
In Group Five, Alberto Elis' 17th-minute goal inspired Honduran side Olimpia to a hard-fought 1-0 victory over Guyanese champions Alpha United.
Meanwhile, defending champions and Mexican giants Cruz Azul played out a 1-1 draw at home to Costa Rica's Alajuelense in Group Six action.