Tina Charles had 22 points and 23 rebounds for the Sun, who got 17 from Renee Montgomery and 16 each from Asjha Jones and Kara Lawson.
The game was tied with a little over two minutes remaining, but Montgomery hit a driving layup with 35.8 seconds left and made two free throws with time running down to seal the game.
Toliver shot 7-for-17 from the field, including 4-for-7 on 3-point attempts. She had four rebounds, three assists and two steals.
The Sparks played their first game without Candace Parker. Parker, who tore the lateral meniscus in her right knee in Sunday's loss to the New York Liberty, will be out for about six weeks.
Parker, averaging 17.7 points and 9.9 rebounds in seven games this season, was limited to 10 games last season because of a shoulder injury.