Brunson began the night in third place with 3,306 rebounds. She passed Lisa Leslie (3,307) early on and overtook Tamika Catchings (3,316) when she grabbed Candace Parker's missed 3-pointer with 7:17 left in the fourth quarter.
Minnesota coach Cheryl Reeve was ejected on the following play for arguing a call, but Brunson was later recognized with a standing ovation from the crowd and a hug from Lynx owner Glen Taylor when the achievement was announced during the ensuing media timeout.
Brunson also had 15 points in her 82nd career double-double, putting her ahead of Yolanda Griffith for sixth on the WNBA career list.
Sylvia Fowles added 27 points, nine rebounds and a career-high seven assists for the Lynx (11-7), who bounced back from their first loss in eight games.
Candace Parker led the Sparks (12-7) with 22 points.