Katie Smith hit a 3-pointer with 1 minute, 13 seconds remaining to put Seattle (14-12) ahead after New York led 62-57.
Sue Bird added 14 points and Camille Little 11 for Seattle.
Jackson, a three-time league MVP, returned after missing 20 games. She played the first five games of the season before tearing a labrum in her left hip.
Plenette Pierson had 15 points for New York (15-12). Essence Carson and Cappie Pondexter each added 12. Pondexter averaged 27.6 points in her previous three games.
Vaughn missed a 13-footer with 6.9 seconds to go that would have given the Liberty a one-point lead. Carson then stole an inbound pass with 3 seconds left but had the ball stripped by Bird as she drove toward the basket and time expired.
Jackson scored the Storm’s first 10 points of the fourth quarter to keep the game close. She fouled out with 4 minutes to go and New York up 57-55.
Pierson and Vaughn had six points apiece in the third quarter to give New York a 49-45 lead. The Liberty outscored Seattle 22-13 in the period.
Kennewick High graduate Leilani Mitchell hit a 3-pointer to give the Liberty its first lead at 39-36 midway through the third quarter.
