Taj Gibson scored 19 points and grabbed 10 rebounds for the Bulls, who were playing without starting power forward Carlos Boozer (sore right knee) and longtime forward Luol Deng, who was traded to Cleveland earlier Tuesday.
In return, the Bulls received Andrew Bynum (who was waived), a first-round pick and a pair of second-rounders.
D.J. Augustin helped out with 13 points and nine assists, and Jimmy Butler also logged 13 points as Chicago notched a third straight win.
The Suns were led by Goran Dragic with 21 points.
Gerald Green added 15 for Phoenix, losers of two in three.
McPhee, Cokas 'working on their marriage' after affair
Attkisson leaves CBS News, reportedly over network's 'liberal bias'