Noah scored 12 points and had four boards in 28 minutes while Boozer added 12 points and nine rebounds in 35 minutes.
While both Noah and Boozer were a go for the Bulls, the Suns got Steve Nash back. Nash, who sat out the past two games with flu-like symptoms, had six points and 16 assists in the loss.
Noah hadn't played since injuring his right ankle against the Philadelphia 76ers on March 28. He missed three games.
Boozer was ill Monday and did not practice.
Noah and Boozer had only played 23 games together before Tuesday, with the Bulls going 18-5.
Nick Friedell covers the Bulls for ESPNChicago.com and ESPN 1000. Information from The Associated Press was used in this report.