Kershaw was ejected for hitting Parra on the right elbow, but the left-hander still got his 19th victory and the Los Angeles Dodgers beat the NL West-leading Diamondbacks 3-2 Wednesday night to snap a three-game losing skid.
The incident was a carryover from Tuesday night's game in which Parra momentarily stood at the plate to admire his solo homer off reliever Hong-Chih Kuo that tied the game in the seventh.
Parra was annoyed Kuo had thrown an earlier pitch near his head, although afterward he said he didn't think it was deliberate.
Dodgers catcher A.J. Ellis yelled at Parra as he crossed the plate, and Kershaw shouted at Parra from the top step of the dugout. The umpires warned both benches against further trouble. The D-backs won 5-4 in 10 innings after scoring on a bases-loaded walk.
Asked if he intentionally hit Parra, Kershaw replied, "No, I didn't mean to."
Kershaw singled out plate umpire Bill Welke for ejecting him, along with manager Don Mattingly in the sixth inning.
"He's too strict," Kershaw said. "Bill is back there just trying to make sure that everything is OK. I understand that he has a job to do, but at the same time, just pay attention to the game and understand what's going on a little bit better."
Kershaw (19-5) allowed one hit over five-plus innings. After Parra's double, he retired the next seven batters in a row and then got ejected.
"I'm not disappointed at all," he said. "We got a win, it was awesome."
After Kershaw was ejected, Mattingly rushed out of the dugout to argue with Welke.
"It was leftover from last night," crew chief Tim Tschida told a pool reporter.
Tschida said Kershaw's pitch was intentional. Told that the Dodgers believed Kershaw was merely pitching inside, Tschida responded, "It's always that view."
Kershaw left the game with a 2-0 lead. There was prolonged booing as he walked to the dugout and took a seat while Mattingly kept arguing.
Mattingly said no official warnings were issued before the game, although Joe Torre, MLB's executive vice president for baseball operations, called his former team to say he didn't want anything to happen.
Asked if he thought Kershaw would be suspended, Mattingly replied, "How do you get suspended for pitching inside, hitting a guy in the elbow that's on top of the plate?"
Arizona's Daniel Hudson (16-10) gave up two runs and five hits in seven innings, struck out four and walked three.
"I still don't think it was on purpose," he said. "A pitch just got away from Clayton and unfortunately, it was to the wrong guy -- the guy who was in the middle of everything yesterday -- and the umpire did what he had to do."
Hudson said the D-backs were contacted by MLB beforehand and given a warning.
"We were told that if they thought there was any intent, we would be ejected and there would be some suspensions," he said.
Parra watched the verbal fray from first base, where he stood with his arms crossed and a smug look on his face.
"I was ready for that. I'm ready for anything. He's pitching, I'm hitting, and that's baseball, man," Parra said. "He's a good pitcher and he has good control, but he threw one pitch inside and then he threw another pitch that hit me. The umpire made the decision, and that's it."
He was booed in his subsequent at-bat when he nearly tied the game with a long ball that right fielder Jerry Sands caught at the wall. Ryan Roberts, who led off the eighth inning with a double, advanced to third after the catch and scored on a broken-bat grounder by pinch hitter Geoff Blum.
Kershaw tied Arizona's Ian Kennedy for the NL lead in victories, the most for a Dodgers pitcher since Ramon Martinez went 20-6 in 1990. The left-hander struck out five, giving him 236 on the season, just two behind Detroit's Justin Verlander for the major league lead.
The Dodgers took a 2-0 lead in the first on RBI singles by Matt Kemp and Sands. They added a run in the eighth on Aaron Miles' RBI single that scored Kemp, who walked and stole second, to help them avoid being mathematically eliminated.
It was Kershaw's second career ejection, and Mattingly's third in his first season as a manager. ... Dodgers RF Andre Ethier underwent arthroscopic surgery in a 35-minute procedure to clean up wear and tear behind his right knee cap. He's expected to begin rehabilitation in a week in Arizona, where he lives in the offseason. ... Kemp notched his 110th RBI, becoming the first Dodger to reach that mark since Adrian Beltre had 121 in 2004. ... Kershaw has won seven straight home starts and each of his past 10 decisions at Chavez Ravine, going 11-1 in 15 home starts. ... The D-backs are 9-6 against the Dodgers, who end the season with three games in Arizona.