The Sun finished the regular season 21-13 and, as the fourth seed, will host a second-round playoff game at Mohegan Sun Arena next Sunday at 3 p.m.
Jones finished the season with 403 rebounds. Tina Charles set the previous league record of 398 in 2010. Charles also played for the Sun when she set the record.
"I just wanted to come into this game and get into my groove as early as possible when it came to rebounding," Jones said. "Just being able to say that I'm able to do something like this is really special. Tina Charles did something special, and to be in the same category as her, it makes me feel really, really good."
With 10 points, Jones finished with 20 double-doubles this season.
"Pretty incredible for a second-year player to break an all-time record like that," Sun coach Curt Miller said. "She's one of the elite rebounders I've ever been around. She just had an unbelievable year at the defensive end, and she's just scratching the surface."
Nneka Ogwumike scored 21 points and Candace Parker had a double-double as the defending champion Sparks (26-8) finished 15-1 at home.
Courtney Williams led the Suns with 19 points.
Lynx 86, Mystics 72: Maya Moore scored 26 points and Renee Montgomery had 18 to help Minnesota secure the top seed in the playoffs with a victory over Washington in St. Paul, Minn.
Minnesota (27-7) has a bye until in the semifinals Sept. 12.
Washington (18-16) is the sixth seed and plays the Dallas Wings in an elimination game Wednesday.
Kristi Toliver hit a three-pointer with 4:28 remaining to pull Washington to 80-71, but Moore answered at the other end, and the Mystics didn't score again until the 2:09 mark.
Toliver led Washington with 20 points. Elena Delle Donne had 12 points in just 18 minutes and Krystal Thomas grabbed 14 rebounds.
Liberty 82, Wings 81: Tina Charles had 18 points and 18 rebounds to help New York clinch the third seed in the playoffs with a win over the Wings in Arlington, Texas. The Liberty finished the season with a 10-game winning streak, matching a franchise record.
The Liberty (22-12) will have a first-round bye. The seventh-seeded Wings (16-18) play at No. 6 Washington in a one-game playoff Wednesday.
Mercury 84, Dream 70: Brittney Griner scored 30 points as Phoenix closed the regular season with a victory over visiting Atlanta, securing the fifth seed in the playoffs.
Phoenix (18-16) will host Seattle on Wednesday night.
Griner reached the 30-point mark for the sixth time in her career with a reverse layup with 1:23 remaining in the fourth quarter. She blocked Elizabeth Williams' shot at the other end. All six of her 30-point games have come this season.
Leilani Mitchell scored 18 points for Phoenix, and Diana Taurasi was held to nine points on 3-for-12 shooting.
Rookie Brittney Sykes scored a career-best 33 points for Atlanta (12-22). She was 12 of 19 from the field and made seven free throws. Tiffany Hayes had 15 points.
Seattle rallied to take a 79-78 lead with 3:11 left as Jewell Loyd's open three-pointer from the corner capped a 9-0 run.
Vandersloot set the record with her seventh assist of the night, finding Jordan Hooper for a three-pointer.