But consider that the Bulls shot 37.5 percent and coach Scott Skiles played reserves Eddie Robinson and Rick Brunson the entire fourth quarter, and you can guess his happiness level with the performance.
Or that of the 16,720 fans, who began booing in the second quarter.
"A win is a win is a win," Skiles said. "But I really feel like missed shots are taking the wind out of our sails defensively. And that can't happen. We have to be mentally stronger."
For the second straight game, the Bulls played a tired road team that entered Chicago after experiencing travel problems.
This time the Bulls were handed the added bonus of the Suns making a major trade earlier Monday that shed them of Stephon Marbury, their leading scorer, and limited them to dressing just eight players.
Still, Phoenix trailed only 81-78 with 90 seconds left before Brunson, playing for a benched Jamal Crawford, came up with a big steal and assisted Jerome Williams on a wild, fast-break layup 10 seconds later.
Brunson followed with two free throws with 16 seconds left. Williams, who had 13 points and 15 rebounds, then rebounded Shawn Marion's missed three-pointer with 10.9 seconds left and iced the victory with two free throws.
Kirk Hinrich led the Bulls with 19 points. Robinson, who didn't play in the first half, scored 10 of his 12 in the fourth quarter.
"It feels good to contribute," Robinson said.
Crawford had six assists but shot 2-for-11 and didn't play after Brunson replaced him with 4 minutes 34 seconds left in the third quarter.
"Maybe I oversimplify it, but everybody has to bring something to the table every game, whatever it is," Skiles said. "That's the expectation I have. Even if a guy is not making his shot but I feel like he's playing well defensively, I tend to leave people out there. I'm looking for consistency of effort and reliability in people."
Barbosa, a rookie who had played 184 minutes all season, took advantage of his first career start to score a game-high 27 for Phoenix.
After losing to Toronto on Sunday, the Suns spent seven hours on an airport tarmac waiting for clearance to fly into snowy Chicago. The Suns never made it, settling for Milwaukee, which meant a bus ride down Interstate 94 on Monday.
"We were all shocked, definitely," forward Tom Gugliotta said. "We were struggling, but by no means did anybody think that they'd trade the heart and soul of our team."
The Bulls are now 1-12 against Western Conference teams.