Goalkeeper Josh Lemos, playing up front in a last-ditch attempt to get the key goal, poked the ball home with five seconds remaining to secure the 6-2 win on the day. El Salvador won the opening leg of the total goals series by a 4-1 margin on Thursday.
El Salvador scored with 30 seconds remaining to take a 6-5 aggregate lead. But the Central Americans could not hold the lead and Matthew Rios scored with 16 seconds left to tie the series 6-6 on aggregate.
Lemos becomes only the third goalie to score in a CONCACAF futsal game.
"This game is about emotion and it just went up and down," said Canadian coach Sipho Sibiya, who has represented Canada in both futsal and beach soccer.
"I'm happy for the boys. They fought hard," he added.
Alvaro Yaques, Louis-Charles Laliberte and Alex Elliot also scored for Canada, which benefitted from an El Salvador own goal.
Canada outshot El Salvador 50-27 (27-11 in shots on target).
Futsal is a five-a-side indoor version of the soccer, played over two 20-minute periods. It is believed to date back to Uruguay in 1930.
Canada joins host Guatemala, Panama and the U.S. in Group A at the regional qualifier, which opens Monday and runs through July 8 in Guatemala City. Group B consists of Cuba, Mexico, Costa Rica and St. Kitts.
"Now we're in the tournament, which is what we wanted," said Sibiya. "That's what we came here to do.
"I told them today we just don't want to be in the tournament now, we want to turn some heads and qualify."
The four semifinalists will advance to the FIFA Futsal World Cup in November in Thailand.
CONCACAF covers North and Central American and the Caribbean.
The Canadian team had little time together prior to taking on El Salvador, other than a camp lasting four to five days in Costa Rica. The Canadian side lost a pair of friendlies to Costa Rica: 2-1 and 4-0.
Canada took part in the inaugural Futsal World Cup in the Netherlands in 1989, when CONCACAF teams received invitations to compete in the indoor world championship.
The Canadians went 1-2 that year, exited after the first round and have never been back since. Canada has not been involved in regional qualifying since 2004.
Sibiya played outdoor soccer for the Vancouver 86ers, Montreal Impact and Edmonton Aviators and had a lengthy career playing indoors. He was an assistant coach with the Vancouver Whitecaps women's team last year.