Shaun Livingston added 21 for the short-handed Clippers, who were playing their first game against an NBA team after two exhibition games in Europe. Quinton Ross scored 13 and Cuttino Mobley had 12.
Leandro Barbosa led the Suns with 19 points and Steve Nash scored 15. Amare Stoudemire, attempting a comeback after playing only three games last season because of two knee operations, scored eight points on 4-of-7 shooting and grabbed a team-high six rebounds in 19 minutes. He missed all four of his free throws.
The Clippers put together a 19-10 surge over the final 6 minutes of the third to take an 83-75 lead going into the final period. Brand was the catalyst, scoring nine of the Clippers' first 11 points during their decisive run.
Los Angeles led by as many as 16 in the fourth quarter.
This was the first matchup between the teams since the Suns defeated the Clippers in seven games in the Western Conference semifinals last season, their first meeting ever in the postseason. The teams will meet again in Phoenix's regular-season home opener Nov. 1.
The Clippers played without forwards Tim Thomas and Aaron Williams, guard Sam Cassell and centers Chris Kaman and Zeljko Rebraca, all of whom are injured.
The teams were tied at 51 at halftime. They combined to shoot 40 free throws in the half, with the Suns making all 19 of their attempts and Los Angeles 16 of 21.