Betts, a six-time Gold Glove winner in right field who made his big league debut in 2014, hit a tying two-run shot off Marcus Stroman in the third inning. He also lined a two-run double to left in the ninth.
"I've been doing the multiple position thing my whole life," Betts said. "It doesn't really matter to me. I just go out and play and want to win."
Betts smoothly handled four grounders at shortstop. The position switch didn't affect him at the plate.
"They're two completely different things," Betts said. "The (batter's) box is the box and defense is defense."
Manager Dave Roberts said Betts could be back at shortstop on Tuesday.
"The more you see him, the more he amazes you. He's a special athlete," Roberts said.
Muncy's fourth homer of the series - a two-run drive off Wrigley's right-field scoreboard in the sixth - lifted Los Angeles to a 4-3 lead. Martinez followed with his fourth homer, chasing Stroman (2-2).
Muncy has 11 homers on the season. He was tied for the big league lead with Mets slugger Pete Alonso heading into Sunday's action.
Muncy hit his 11th homer last year on Aug. 6 and finished with 21. The third baseman said he is seeing the ball "extremely well."
"Just being able to be free in the box allows me to recognize things so much easier," he said.
Muncy's homer helped atone for a first-inning error that led to two unearned runs for Chicago.
Stroman yielded six hits - including three homers - and walked one in five-plus innings. He allowed a total of two runs in his first four starts.
"The last two pitches, I got out of whack mechanically and I paid for it," Stroman said. "Until then, I felt great."
Kershaw was charged with three runs, one earned. The left-hander struck out six and walked one.
Brusdar Graterol pitched two innings for his first save.
Chicago scored two in the first on RBI singles by Bellinger and Seiya Suzuki. The rally was set up when Muncy couldn't come up with leadoff man Nico Hoerner's hard grounder to third.
BETTS AT SHORTSTOP
Betts started a game-ending double play after the Cubs loaded the bases in the ninth. Betts, who was drafted as a shortstop, made his first big league appearance at the position on Thursday.
Roberts said he wanted to get Betts' bat into the lineup, especially since Chris Taylor has been dealing with an oblique injury and struggling at the plate.
Stroman recorded his 1,000th career strikeout when he got Freddie Freeman looking in the third.
Dodgers: RHP Tony Gonsolin (sprained left ankle) might be in line to start Wednesday in Pittsburgh, Roberts said. ... C Will Smith (concussion) missed his 10th straight game, but ran before Sunday's game.
Cubs RHP Kyle Hendricks (right shoulder strain) pitched three innings in an extended spring training game on Saturday. He'll toss a bullpen session on Tuesday and then is expected to go on a rehab assignment, manager David Ross said. ... RHP Codi Heuer (Tommy John) tossed an inning of a simulated game on Saturday.
AP MLB: https://apnews.com/hub/MLB and https://twitter.com/AP--Sports