Rockies center fielder Brenton Doyle won for the second straight season.
It was Chapman's first Gold Glove in the NL. He won three with Oakland and one playing for Toronto.
St. Louis slugger Nolan Arenado, a 10-time Gold Glove winner, and Colorado's Ryan McMahon also were finalists at third.
"A lot of really good defensive third basemen are stacked in the National League," Chapman said in a video call. "I was able to come over here and win it, so I thought that was pretty cool and to get one in the American League and the National League now means a lot."
Six teams had two Gold Gloves winners each, with the Guardians joined by Colorado, Kansas City, Milwaukee, San Francisco and Seattle.
AL first-time winners in addition to Witt include Royals pitcher Seth Lugo, Mariners catcher Cal Raleigh, Minnesota first baseman Carlos Santana, Houston third baseman Alex Bregman, Toronto center fielder Daulton Varsho, Boston right fielder Wilyer Abreu and Mariners utilityman Dylan Moore.
NL first-time winners included Atlanta pitcher Chris Sale, Giants catcher Patrick Bailey, Milwaukee second baseman Brice Turang and right fielder Sal Frelick, Colorado shortstop Ezequiel Tovar and Pittsburgh utilityman Jared Triolo.
Frelick and Turang are the first Brewers to win a Gold Glove since Lorenzo Cain in 2019. They are the second set of Brewers teammates to win Gold Gloves in the same season, joining Cecil Cooper and Sixto Lezcano in 1979.
"It's obviously an honor," Frelick said. "A little surreal, still. Obviously I think even cooler to do it with Brice."
Bregman earned a $50,000 bonus, Giménez, Lugo, Moore and Witt $50,000 and Santana $25,000.
There also were 14 first-time winners in 2022.
Voting was conducted among managers and up to six coaches from each team, who can't select players on their own club. Since 2013, voting has been factored with a Society for American Baseball Research defensive index, which comprises about 25% of the total.
The utility category is based on a SABR formula and additional defensive statistics.