Griffin had 22 points and 10 rebounds and Jordan had 20 points and 11 rebounds to lead six players who scored in double figures while helping the Clippers snap a two-game skid against the team that swept them out of the second round of the playoffs last season.
Danny Green scored 12 points and Tim Duncan added 10 for the Spurs, whose 4-0 start was the best in franchise history.
Jordan, Griffin and Chris Paul, who had 10 points and 12 assists, left the game for good with 4:47 remaining and the Clippers ahead by 25 points. They had just finished a raucous stretch of dunks off alley-oop passes during a 12-2 spurt. Griffin had three big dunks in the sequence after Jordan's high-flying act dominated the third quarter.
The Spurs got no closer than 11 points after opening the fourth on an 11-2 run. Jamal Crawford hit a 3-pointer to reignite the Clippers' offense.
The Clippers took an 82-62 lead into the fourth after outscoring the Spurs 35-21 in the third while shooting 71 percent from the field. Los Angeles dominated the defensive glass 12-2 and its second unit extended the lead to 20 points while Griffin and Paul spent the last few minutes on the bench.
Eric Bledsoe led Los Angeles' reserves with 15 points and Matt Barnes added 12.
Jordan had three highlight dunks in the third quarter, including a fast break off an alley-oop pass from Paul. The Spurs were held to 37 percent shooting and outscored 22-10 in the paint.
The Clippers led 47-41 at halftime after being ahead by 11 points early in the second. They had just six turnovers after committing 13 in the first half against Cleveland in their previous game. Griffin, Paul and Jordan propelled the Clippers' offense in the second quarter, with Jordan scoring eight points, including consecutive dunks, and Griffin and Paul four each.
Notes: G Manu Ginobili scored nine points playing in his 670th game as a Spur, moving him into fifth on the franchise's all-time list. ... Griffin played with a sleeve covering his right elbow for the second straight game. He has fluid on his elbow and a stiff neck. ... The Spurs' loss left the Knicks as the NBA's only undefeated team. ... Billy Crystal and Floyd Mayweather Jr. were among the Clippers' fourth sellout crowd of the season and 53rd in a row.