Grant Hill had 19 points and 13 rebounds, Leandro Barbosa added 17 points, Amare Stoudemire 16 and Channing Frye 12 for the Suns, who won their fifth in a row over the Clippers after a four-game sweep last season.
"Primarily because this was our first game of the season and we're really not sure how good we can be yet, it was just a big win for our confidence," Nash said. "We won it with some timely execution and a few stops."
No one was timelier than Nash.
The Suns trailed by seven early in the fourth before he took over, scoring seven in a row to pull them into a tie at 104 with 1:41 remaining.
After a timeout, Barbosa hit a 3-pointer in front of the Clippers' bench to put Phoenix ahead 107-104 for the first time since early in the third quarter.
Rasual Butler answered with a 3-pointer from the top of the key for the Clippers, tying it at 107 with 11 seconds left.
"I had a good look and launched it," he said. "We were looking at the 3, but if the drive was there we would take the quick two and foul."
Nash drove through traffic in the lane and hit a layup to put Phoenix back on top 109-107 with 5 seconds to go. He was called for a foul, resulting in the Clippers getting the ball out of bounds, but they couldn't muster the winning 3.
"I went to the old-white-guy-at-the-YMCA shot and I was lucky to make something happen," Nash said. "We scrapped, we fought and we swung the ball to L.B. for a big 3 as well. It was a great effort."
Stoudemire played his first game since Feb. 18, on the same court and against the same opponent. The All-Star forward underwent surgery to repair a detached retina in his right eye, which kept him out of the final 29 games last season.
He, Nash, Barbosa and Hill are among the veteran holdovers from D'Antoni's era. Among the newcomers are Frye and Earl Clark. The Suns' running game didn't materialize with the mix of old and new. Phoenix managed just two points on fast breaks, compared to 16 for the Clippers.
"It would be nice if we could get some easy buckets, but it's difficult for us sometimes because we've got a lot of different players from when Mike D'Antoni was here," Nash said. "Those days are over, and we've got to find a way to kind of pull it back out of ourselves with the new guys and get everyone kind of accustomed to that."
Marcus Camby had 23 points and 11 rebounds for Los Angeles, which dropped to 0-2 after losing its opener 99-92 to the NBA champion Lakers a night earlier. Chris Kaman added 22 points, including six straight over the final 4:02, to keep the Clippers in it until the end.
Eric Gordon added 16 points, but he missed a potential game-winning 3-pointer with Stoudemire guarding him closely in the closing seconds. Butler scored 19 points and Baron Davis had 12 points and 12 assists.
"We missed a lot of free throws (15 of 27) and one play I missed a layup," Gordon said. "They made a lot of plays and made shots."
The Clippers are two losses into a six-week stretch without No. 1 overall draft pick Blake Griffin, who has a broken left kneecap.
"We need to play with energy, a sense of urgency and some fire," Butler said. "We need to continue to play hard, defend and make free throws."
The teams were tied at 53 going into halftime. The Clippers built a 10-point lead midway through the third quarter, but saw it dwindle to two when they were outscored 12-5 to end the third ahead 79-77. The Clippers led by nine in the opening quarter.
Dressed in a suit and tie, Blake Griffin addressed the crowd before the game, thanking them for their support and saying, "Hopefully [we] give you a season you won't forget." His older brother Taylor, a rookie forward for the Suns, was inactive for the game. ... The Griffin brothers' mother Gail wore a jersey divided down the front with each team's logo.