McBride, who missed the first four games of the season finishing up playing in Turkey, made 4 of 7 from 3-point range, Jefferson finished with seven rebounds, six assists and four steals and Fowles added 12 rebounds and two blocks. Jessica Shepard finished with 10 points and nine rebounds.
Minnesota (1-4) avoided its first season-opening five-game losing streak since 2007. The Lynx began the 2021 season with four consecutive losses before finishing the season with 22 wins, third most in the WNBA.
Nneka Ogwumike missed a driving layup for the Sparks but grabbed her own offensive rebound and kicked it out to Lexie Brown for a 3-pointer to make it 84-all with 53.3 seconds to play. Shepard's putback off a missed layup by Jefferson put the Lynx back in front 19 seconds later but Liz Cambage was fouled as she hit a shot in the lane with 15.1 remaining. She missed the free throw.
McBride was fouled as she made a reverse layup and converted the three-point play to cap the scoring with 2.1 seconds left.
Ogwumike led Los Angeles (2-3) with 22 points and grabbed eight rebounds. Cambage and Brown scored 12 points apiece.
Jefferson, who was recently waived by the Dallas Wings, was signed by Minnesota on Friday.
Kayla McBride's reverse and-1 gives Lynx first win of season
The Lynx spoil the Sparks' home opener after Kayla McBride's and-1 bucket.