Barbosa scored 25 points, including 5-of-7 on 3s, Hill added 24 points and Phoenix pulled away to win its fourth in a row, 112-102 against the Chicago Bulls on Thursday night.
Hill's performance came on the heels of his 21-point effort against New York two nights earlier.
In between, he flew with his wife, Tamia, by charter flight to Chicago for an appearance on Oprah.
"I'm starting to get my legs, starting to turn the corner there, and just find a rhythm," he said. "It's a process, but I feel good now and just want to keep looking to get better."
Shawn Marion, who scored 11 of his 21 points in the final 6½ minutes, admitted his nerves were shook up a bit after being involved in a car accident on his way to the arena.
"I almost sat out the second half because I wasn't feeling right at all," Marion said. "It didn't hit me until afterward that I was in a wreck before the game. My team helped me, coach and everybody kept telling me to just take deep breaths and go out there and get it done."
Steve Nash had 10 points and 15 assists for the Suns, and Stoudemire added 14 points.
"We had our ups and downs a little bit," coach Mike D'Antoni said. "Boris had a start that was bad, but he came on and his fourth quarter was great. That's what we have to have."
Nash had seven assists in the fourth quarter.
"Steve came in and kind of regained control of the game for them," Chicago coach Scott Skiles said, "and we didn't have much of an answer for it."
"I thought we played hard, but toward the end of the game and throughout the game we made some bad decisions," Gordon said. "We've just got to shore some things up."
At least this game was an improvement, said Skiles, whose team was blown out at home by 30 points against Toronto in their last game, at home on Saturday.
"There were stretches for longer time periods where we played a little bit higher-quality basketball, that's for sure," Skiles said, "but we're not in this to do that. We're in this to try to win the game."
Diaw's three-point play with 7:28 to go put Phoenix ahead for good, 88-85. The Bulls scored to get within one, then Marion's inside basket on a pass from Hill triggered a 9-0 run that put Phoenix in control for good.
The decisive spurt featured Barbosa's final 3-pointer, on a kickout pass from Nash on a fast break, to give the Suns a 93-87 lead with 6 minutes to play.
The Suns shot out to a 15-6 lead and were up by 15 in the second quarter.
But the Bulls finished the third with an 11-1 run to tie it at 75 on Kirk Hinrich's 16-footer with 21 seconds to go in the period. Chicago took a 76-75 lead when Tyrus Thomas made one of two free throws to start the fourth.
There were four lead changes and five ties before Diaw's three-point play.
Barbosa, who scored 16 in the second quarter, hit three consecutive 3s in an 11-3 spurt that put the Suns ahead 56-41 with 1:09 left. But Gordon sank a 3-pointer and Deng added a layup to cut it to 56-46 at halftime.
Hill, who shot 7-for-8 in Phoenix's victory against New York on Tuesday, had 17 in the first half against Chicago, 11 in the second quarter.
Five consecutive points by Marion, on a 3-pointer and a driving runner, gave Phoenix a 62-48 lead before the Bulls launched their rally.
Signed as a free agent in the offseason, Hill has quickly acclimated to the Suns' ultra-up-tempo style. He had a fast-break layup on a half-court lob pass from Barbosa, the last of his six consecutive points that put Phoenix ahead 36-32.
- Skiles started Andres Nocioni in place of Thomas and expects to stay with that lineup at least through this weekend.
- Raja Bell was back in the Suns lineup after missing two games because of a sprained right ankle.
- Stoudemire will turn 25 on Friday.
- Chicago assigned rookie guard JamesOn Curry to Iowa of the NBA Development League.