Ebony Hoffman scored a game-high 21 points leading Fever, 75-70.
Candace Parker added 18 points, six boards and five assists for Los Angeles, which was coming off a home loss to Atlanta on Tuesday.
Erin Phillips and Tamika Catchings each netted 16 points for Indiana, which had its three-game win streak snapped. Tangela Smith chipped in 14 points and nine rebounds in defeat.
Parker's three-point play with 3:13 remaining gave LA a 68-66 lead, and the Sparks hit enough free throws down the stretch to hang on.