Cappie Pondexter hit the winning jumper with 81.
After Kalana Greene put in a running layup with 62 seconds left to give the Sun an 81-80 lead, New York was called for an offensive foul, but a bad pass from Renee Montgomery gave the Liberty the ball back and Pondexter hit a pull- up jumper for a one-point lead with 24.3 seconds to play.
Connecticut then missed on three separate shots on its next possession with Plenette Pierson finally grabbing the defensive board.
After Pondexter missed both her shots at the free throw line, a turnover and personal foul from Tan White let Essence Carson seal the win with two free throws.
Pondexter had 27 points and six rebounds while Carson added 19 points and eight boards for the Liberty, who have won two straight.
Tina Charles had 29 points and 14 rebounds for the Sun, who had won two straight coming into the game. Renee Montgomery added 16 points and five assists in the loss.
The Sun held a 15-point lead going into the fourth, but stormed the fourth quarter with Pondexter giving the team a 74-71 lead with 50.2 seconds to play on a three-pointer. Kara Lawson countered with a three of her own to send the game to overtime.