Eric Bledsoe led the Clippers with 25 points, including a reverse layup with 3.1 seconds left that tied it.
Blake Griffin, who had surgery on his left knee in the offseason, had six points and seven rebounds in 22 minutes.
Chris Paul did not play for Los Angeles. He is expected to be cleared for full contact practices within two weeks.
The game was played on The Las Vegas Strip for the first time since 1981 when the Los Angeles Lakers faced Philadelphia.