The Sparks roared back with 12 straight points after Leslie fouled out, then held off a late rally to beat the Shock 63-60 in a rematch of last year's WNBA Finals.
Leslie committed her sixth foul with 2:35 remaining, and Detroit forward Cheryl Ford made 1-of-2 free throws to give the Shock a 57-51 advantage.
Consecutive 3-pointers by Nikki Teasley and Tamecka Dixon tied the game and a jumper by Mwadi Mabika with 46 seconds left gave L.A. its first lead since 2-0.
Los Angeles made four straight free throws for a 63-57 lead before a banked 3-pointer by Swin Cash and two misses at the line by Mabika gave Detroit a chance to tie with three seconds remaining. However, Deanna Nolan's 3-pointer from the corner bounced off the rim as time expired.
Teasley scored 15 points and Leslie added 12 on just 4-of-16 shooting for the Sparks (2-2), the only team yet to play a home game.
Cash scored 17 points and Nolan 16 for the Shock (1-2) in their home opener.