Quentin rushed the mound after he was hit in the upper left arm by a pitch from Zack Greinke. The two players lowered their shoulders and Quentin slammed into Greinke, breaking the pitcher's left collarbone.
Hairston incited a second melee when he ran across the field gesturing at someone in the Padres dugout.
Quentin and Hairston are playing, pending appeal by the players' association.
Quentin also was fined $3,000. Hairston was fined, too, but the amount wasn't immediately known.
No discipline was announced for Greinke or Matt Kemp, both ejected along with Quentin and Hairston.
MLB is believed to be investigating Kemp's confrontation with Quentin as the players were leaving Petco Park after the game. The two went nose to nose before Padres pitcher Clayton Richard got between them. Police and security moved in and broke it up.
Greinke is scheduled to have surgery Saturday and miss eight weeks.