Shoni Schimmel set a season-high for the second straight game with 21 points, none bigger than a jumper with 6 seconds left in regulation to force a 52-all tie that carried into overtime.
Slaughter hit her 3-pointer 13 seconds into overtime, and Sara Hammond followed with a trey about a minute later for a 58-52 lead. Schimmel tacked on a jumper and Slaughter a free throw for a 61-52 lead with 40 seconds to play.
Monique Reid added 18 points for Louisville (13-3, 1-1).
Erica Wheeler paced Rutgers (9-6, 0-2) with 18 points. Monique Oliver, who has been battling a sprained left ankle, scored 10 points with nine rebounds in 36 minutes.