On July 27, 2015, Crowder re-signed with the Celtics to a reported five-year, $35 million contract. On December 18, 2015, he scored a career-high 24 points in a loss to the Atlanta Hawks. He topped that mark on January 4, 2016, scoring 25 points in a 103–94 win over the Brooklyn Nets. On January 13, he tied his career high of 25 points in a 103–94 win over the Indiana Pacers. On March 14, he was ruled out for two weeks with a right ankle sprain. He returned to action on March 31 against the Portland Trail Blazers after missing eight games. In the Celtics' season opener on October 26, 2016, Crowder scored 21 points in a 122–117 win over the Brooklyn Nets. He appeared in the team's first four games of the season, but then missed eight straight games with a sprained left ankle. He returned to action on November 19, scoring nine points in a 94–92 win over the Detroit Pistons. On March 17, 2017, he recorded season highs with 24 points and 12 rebounds in a 98–95 win over Brooklyn. On March 26, 2017, he set a new season high with 25 points in a 112–108 win over the Miami Heat. In Game 1 of the Celtics' Eastern Conference semifinal match-up with the Washington Wizards, Crowder scored a playoff career-high 24 points, helping the Celtics win 123–111. On August 22, 2017, Crowder was traded, along with Isaiah Thomas, Ante Žižić and the Brooklyn Nets' 2018 unprotected first round pick, to the Cleveland Cavaliers in exchange for Kyrie Irving. Eight days later, the Celtics agreed to send the Cavaliers a 2020 second-round draft pick via the Miami Heat to complete the trade. On November 20, 2017, Crowder scored a season-high 18 points against the Detroit Pistons. On February 8, 2018, Crowder was acquired by the Utah Jazz in a three-team trade that also involved the Cavaliers and the Sacramento Kings. In his debut for the Jazz three days later, Crowder scored 15 points in a 115–96 win over the Portland Trail Blazers. On March 9, 2018, he scored a season-high 22 points in a 95–78 win over the Memphis Grizzlies. In Game 5 of the Jazz's first-round playoff series against the Oklahoma City Thunder, Crowder scored a career playoff-high 27 points in a 107–99 loss. On January 1, 2019, Crowder scored a career-high 30 points in a 122–116 loss to the Toronto Raptors.