Channing Frye's 3-point bucket with 41.6 seconds left on the clock proved to be the game-winner for the Suns, who won their eighth in a row and returned to the playoffs after failing to make the cut last season.
Chicago had tied the game 103-103 with just under a minute to play on a pair of free throws by Derrick Rose. Frye responded with his decisive 3-pointer from the top of the arc.
Jason Richardson led Phoenix with 27 points and Steve Nash added 22, including nine in the fourth quarter. Amare Stoudemire scored 21 and grabbed 11 rebounds while Frye finished the night with 12 points.
The Bulls were led by Derrick Rose and Flip Murray, who both scored 23 points. Chicago fell 1 1/2 games behind Toronto in the race for the final playoff spot in the Eastern Conference.