Seattle manager Scott Servais, Los Angeles interim manager Phil Nevin and six players were ejected after the brouhaha, which stopped and started twice before Angels closer Raisel Iglesias came back out to the empty field to throw large containers of sunflower seeds and gum onto the infield.
The Mariners' Winker was hit by the first pitch of the second inning by Angels opener Wantz, who also had thrown a pitch behind the head of Rodriguez in the first inning.
The first pitch to Rodriguez appeared to be a response to Erik Swanson's 95 mph fastball near Mike Trout's head in the ninth inning Saturday night, a throw that infuriated the three-time American League MVP. The umpires gathered together after Wantz's pitch but only issued warnings to both dugouts.
"That probably shouldn't happen in the game, what happened out there today," Servais said. "Emotions running high, but it was pretty clear what was going on. They switched, put an opener in there to throw some balls at us. Got out of hand from there, and kind of a black eye."
Wantz insisted it wasn't retaliation.
"I was pretty amped up for my first start, and the first one just got away from me," Wantz said. "It was sweaty. I was sweating. First day game I've pitched in [in the majors], and that's that. Second one to Winker was a cut fastball inside, and [I] just yanked it. That's all I've got to say."
Winker reacted to getting hit by angrily yelling and gesturing at the Angels' dugout, and the sides charged each other moments later, with both benches and bullpens emptying. The brawl lasted about four minutes, with people from both teams appearing to throw multiple punches.
Injured Angels star Anthony Rendon threw an open left hand to Winker's face during the scuffle, which is notable because his right hand is in a cast. The Halos' $245 million third baseman is already out for the year for the second straight season.
When Winker finally left the field, he made obscene gestures with both hands at the jeering Angels fans behind the Seattle dugout.
"The only thing I'm going to apologize for is flipping the fans off," Winker said. "That's it. As fans, they're spending their hard-earned money to come watch us play a game, and they didn't deserve that, so I apologize to the fans, especially the women and children."
After the teams returned to their dugouts, Iglesias returned a few moments later to throw the sunflower seeds and gum while furiously screaming at the umpires, infuriated by his ejection.
Servais and Seattle starter Marco Gonzales both felt the umpires erred by not ejecting Wantz immediately.
"I'm not aware of the incident with Trout from last night," crew chief Adrian Johnson told a pool reporter. "You're talking about the pitch that went over his head. That was nothing for us to issue warnings today. What happened today was a guy got hit. We had warnings in."
The scoreless game was delayed about 18 minutes, and it resumed with pinch runner Adam Frazier on first for Seattle and Jose Suarez on the mound for Los Angeles. The rest of the game went off without incident as the Angels won 2-1, avoiding being swept at home after they won four of five in Seattle last week.
"Look, you play eight games in a matter of a week against the same team, things like this happen," Nevin said after L.A.'s eighth game in 11 days against Seattle. "The scheduling, tensions, that's baseball sometimes, unfortunately. There's some ugly incidents once in a while. I think that's just what happened today."
The Associated Press contributed to this report.