Brawley's lone goal came from Ernie Torres in the first overtime.
Said Wildcat coach Frank Felix: "This was a good game overall, very exciting and fun to coach. I was real pleased with my team's performance because they played real well the entire game."
Both teams play Thursday, with Brawley (2-4-1 overall, 0-1 IVL) playing at Holtville at 5 p.m. and Southwest (6-2-3, 1-0) hosting Yuma at 4 p.m.
Calexico 1, Central 0
The Calexico High School boys soccer team opened IVL play with a 1-0 win over Central Union at Cal Jones Field in El Centro on Tuesday.
The Bulldogs return to action at 6:30 p.m. Friday at Palo Verde High in Blythe. Central (3-6-2) will next play Dec. 27 in the Oceanside tournament.
Central 0, Calexico 0
The Central Union High School soccer team played Calexico to a 0-0 tie in both teams' Imperial Valley League opener Tuesday.
The game was played at Cal Jones Field in El Centro.
Clarissa Maldonado had the shutout in goal for the Spartans (3-5-1).
Both teams return to action Friday. Central will play at the Chula Vista tournament, Calexico will host Palo Verde at 6:30 p.m.
Brawley 1, Southwest 0
The Brawley Union High School girls soccer team edged Southwest 1-0 in IVL action in El Centro on Tuesday.
In the 36th minute of the second half, the Wildcats' Melissa Carrillo scored the only goal of the game.
Brawley's Maria Sarmiento had four saves to record the shutout for the Wildcats.
Brawley returns to action at 5 p.m. Thursday at home against Holtville. Southwest returns to action at 6:30 p.m. Friday at Imperial.