Kennedy hit Puig with a pitch that deflected off his back to his nose in the sixth, and Greinke hit Montero on the back in the seventh, drawing a warning from umpires. Both teams charged onto the field, but the scrum broke up quickly with no punches thrown.
Kennedy then hit Greinke on the upper left shoulder in the bottom half of the inning, and the ball deflected off his helmet. A prolonged and more heated scuffle ensued against a railing on the first base side.
Montero, joked that he kept getting hit at the bottom of the pile but "obviously they are probably my teammates that were punching me because we're the only ones who got suspended" but isn't sure why Greinke was spared a suspension.
"Ian got 10 days and Zack got zero days when he admitted that he hit me on purpose, seriously?" Montero said. "'We just give him a fine because he was already seven weeks out.' Well, he can miss one more. C'mon. Give me a break with that."
Kennedy, Gibson and Diamondbacks coach Turner Ward were ejected after the shoving match. Puig, McGwire and Dodgers reliever Ronald Belisario also were tossed.
Mattingly had to be restrained as he tried to get at Gibson, and they exchanged words briefly. McGwire and third base coach Matt Williams grabbed each other's shirts in a tense standoff and shouted at each other.
Mattingly said he was only playing "peacekeeper" and understands the fight will likely have some carryover effect, even if it is only in the media.
"There's no way for us to go to Arizona now without us having to talk about it," he said. "There's going to be an effort to keep it alive and it won't be by the players or us."