The Raiders (19-7) built leads of 20-12 after one quarter and 38-26 after two on the way to their first tourney win in their third appearance.
They still led by 11 early in the fourth quarter, but the Razorbacks (19-9) kept chipping away.
Third-team All-American Chelsea Dungee hit a 3-pointer with 1:50 to go for a 59-58 lead.
But Alexis Stover hit a 3 for the Raiders, and Baker buried a trey with 29.1 seconds left for a 64-62 lead.
Arkansas then missed, and Baker snagged the rebound.
Jada Roberson was fouled and made two free throws with 8.1 seconds left for a 66-62 lead.
The Raiders were overmatched in their first two NCAA games, losing by 46 to Kentucky and 23 to Texas A&M.
The Raiders will advance to the second round against fifth-seeded Missouri State (22-2) on Wednesday at a time and site to be determined. The Lady Bears beat UC Davis, 70-51.
The winner will meet either top-seeded Stanford or Oklahoma State in the Sweet 16.
THAT’S A RAIDER NCAA WIN!!! 🐺#RaiderUP | #RaiderFamily | #ncaaW pic.twitter.com/UUywk58WBr
— Wright State Women’s Basketball (@WSUWBasketball) March 22, 2021
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