Considering the brutal schedule they have played in their first six games, the process hasn't been easy.
The Hawks suffered their first loss after a 6-0 start. The Suns (3-3) took their second straight win.
The Hawks were the Suns' fifth opponent coming off a 50-win season.
The Suns are working on a new look inside after losing Stoudemire, the power forward who signed with the New York Knicks.
"It's going to take us a month, two months, to get to the point where we really know who we are," said Nash, who had 15 assists.
"The biggest thing is cohesion. It's just going to take a little time. ... I think we're getting better. We're not there yet but we're getting better."
Hedo Turkoglu, more accustomed to a perimeter game, had 11 points and four rebounds at power forward.
"This is not my position," Turkoglu said. "I never played it before."
There were four ties in the fourth quarter but the Hawks, who trailed by 18 in the third period, could not take the lead.
"Down the stretch we couldn't get the key stops we normally get on defense," said Joe Johnson, who led Atlanta with 34 points.
Nash made four free throws in the final seven seconds to protect the lead.
Al Horford added 30 points -- one shy of his career high -- and 10 rebounds for Atlanta. Johnson and Horford each set season scoring highs.
"I don't think anybody in the league works harder than Horford does on either end of the floor," said Suns coach Alvin Gentry. "Whatever they signed him for, it's a bargain. He's a stud."
Horford and the Hawks agreed to a five-year, $60 million contract extension on Monday.
After trailing through the second half, the Hawks pulled even at 106 on two free throws by Jamal Crawford, who had 11 points, with 2:29 remaining.
Nash scored on a fallaway jumper with 1:07 remaining for a 112-110 lead. Crawford's jumper pulled the Hawks even for the third time in the period.
Channing Frye's one-handed bank shot over Mike Bibby gave Phoenix a 114-112 lead with 24 seconds remaining. Johnson, surrounded by Phoenix defenders, missed a short jumper with 9 seconds left. Nash made two free throws with 6.7 seconds left to push the lead to four points.
The Hawks were denied in their attempt for their first 7-0 start since winning their first 11 games in the 1997-98 season.
"It was a clear case how badly we needed a Marvin or Mo so we could go smaller," Drew said.
The Suns snapped the Hawks' streak of 14 straight home wins, the longest active streak in the league. The Hawks' last home loss was an 111-103 overtime loss to Dallas on Feb. 26.
The Suns took a big lead of 18 points at 79-61 in the third quarter on a 3-pointer by Richardson. The Hawks made a strong rally by making their last 10 shots of the third quarter, including six 3-pointers.
"For them to come back like they did and for us to maintain our poise was very important," Gentry said.
After the third period, officials reviewed a basket by Nash with 3:43 remaining and ruled he scored after a 24-second violation. The ruling left the Suns' lead at 90-88 instead of 92-88 entering the final period.
Josh Childress had 11 points in his first game at Philips Arena since he left the Hawks following the 2007-08 season to play two years in Greece. Childress averaged 11.1 points in four seasons with Atlanta.
Josh Smith had 19 points, 9 rebounds and 4 assists.
The Phoenix bench, led by Jared Dudley's 15 points, outscored Atlanta's backups 46-19. ... Smith had a blocked shot to pass Dikembe Mutombo (1,094) for second place on the Hawks' career list. ... Drew said Williams is expected to miss about a week with the bone bruise in his right knee he suffered on Friday. Drew said Williams is still a little sore "but a lot better at this stage than what we thought it would be." ... Williams wore a three-piece suit with a bow tie on the Hawks' bench.
While Draymond Green's latest kick has been heavily scrutinized, his distinct kicking motion as he drives has been a part of his game all season.
Michael Wilbon and Marc Stein evaluate the NBA's decision not to suspend Draymond Green for kicking Steven Adams in the groin during Game 3 of the Western Conference finals.