Los Angeles outscored Seattle 30-10 in the fourth quarter, taking its first lead of the game on Toliver's baseline reverse layup with 1:38 remaining. The Sparks had lost seven of their previous nine games against Seattle.
Candace Parker added 11 points for Los Angeles, including a pair of key baskets in the comeback, and a tough shot in the lane with 28 seconds left.
Ann Wauters led Seattle with 17 points, and Sue Bird had 15.
Toliver was brilliant providing Los Angeles the energy off the bench they lacked in the early going when Seattle jumped to an 11-0 lead and appeared on the verge of turning the game into a blowout. Toliver was 9 of 16 from the field and was even left shaking her head after a 3-pointer from the top of the key with a minute left took a favorable bounce off the rim and fell through.
Nneka Ogwumike, the No. 1 overall pick in the WNBA draft, finished with nine points - all in the second half. Alana Beard added nine points for Los Angeles as well.
Los Angeles' massive rally started with a 10-2 run spanning the third and fourth quarters, pulling to 56-48 with 7:54 left on DeLisah Milton-Jones' jumper. Jantel Lavender hit a baseline jumper for the Sparks, and Toliver scored on a drive to cut Seattle's lead to 56-52. After Tina Thompson's 3-pointer rimmed out for Seattle, Beard converted a difficult left-handed layup while being fouled. She missed the free throw, but the lead was just two.
Bird answered with a baseline layup with 5:29 left, Seattle's first points of the fourth quarter. Seattle's lead was back to 62-56 with 4:20 left when Tanisha Wright scored on a fast-break layup, but the Storm were outscored 16-4 the rest of the way.
Parker's tip of her own miss with 2:58 left pulled Los Angeles even at 62-all. After an exchange of missed 3s, Wauters was fouled on the baseline, but could only split the free throws. Toliver then got free on the baseline for a reverse layup and the Sparks' first lead. Toliver padded the advantage with a 3 and despite Camille Little's three-point play for Seattle, Parker's basket with 30 seconds proved to be enough.
Thompson finished with 12 points in her first game with Seattle. After hitting nine of 14 shots in the first quarter, Seattle was 16 of 43 (37 percent) the rest of the way.