Tina Charles scored 17 points and pulled 92.
Asjha Jones added a double-double with 16 points and 11 boards, and Kalana Greene, Renee Montgomery and Kara Lawson each dropped in 14 points in the Sun's fourth win in six games.
Phoenix got WNBA leading scorer Diana Taurasi back after missing two games with back spasms, but her 26 points were not enough to stop the Mercury from losing their second straight game.
Penny Taylor also scored 26 points for Phoenix, which lost its fourth straight contest against Connecticut.
With under two minutes to play and the score tied at 86, Taurasi and Taylor each missed three pointers before Lawson dropped a shot from beyond the arc to put the Sun ahead for good.
A Taurasi three brought the Mercury within one at 93-92 with 4.1 seconds to go, but after Lawson made two free throws, Taurasi missed the game-tying shot as time expired.