In Game 4 of the Eastern Conference Finals against the Boston Celtics, Irving scored a playoff career-high 42 points to lead the Cavaliers to a 112–99 win, taking a 3–1 lead in the series. With 24 points in Game 5 of the series, he helped the Cavaliers defeat the Celtics 135–102 to claim their third straight Eastern Conference title and a return trip to the NBA Finals. After going down 3–0 in the 2017 NBA Finals, Irving scored 40 points in Game 4 to help Cleveland extend the series and avoid a sweep with a 137–116 win over the Golden State Warriors. The Cavaliers went on to lose to the Warriors in Game 5, thus losing the series 4–1.
In July 2017, Irving requested the Cavaliers to trade him, reportedly wanting to be more of the focal point of his own team instead of continuing to play alongside LeBron James. The next month, on August 22, he was traded to the Boston Celtics in exchange for Isaiah Thomas, Jae Crowder, Ante Žižić, and the rights to the Brooklyn Nets' 2018 first-round draft pick. Eight days later, the Celtics agreed to send the Cavaliers a 2020 second-round draft pick via the Miami Heat to complete the trade, as compensation for Thomas' failed physical.
In his debut for the Celtics in their season opener against the Cavaliers on October 17, 2017, Irving had 22 points and 10 assists in a 102–99 loss. He had a chance to tie it with a 3-pointer at the horn but missed. On October 30, 2017, he scored 24 points for the third straight game in helping the Celtics defeat the San Antonio Spurs 108–94. It was the Celtics' first win over the Spurs since 2011. Irving's 128 points in his first six games as a Celtic were the most since Kevin Garnett and Ray Allen each had 131 in 2007. On November 6, 2017, he scored 35 points in a 110–107 win over the Atlanta Hawks, recording his first 30-point game as a Celtic while scoring more points (245) than any player in his first 11 games with Boston. With the win over Atlanta, the Celtics improved to 9–2 with nine straight wins, setting their longest winning streak in seven years. On November 20, 2017, he scored 10 of his season-high 47 points in overtime as the Celtics rallied from a double-digit deficit to beat the Dallas Mavericks 110–102, extending their winning streak to 16 games. The streak ended at 16 games with a loss to the Miami Heat two days later. On January 21, 2018, he scored 40 points in a 103–95 loss to the Orlando Magic. The Celtics had accumulated a 34–10 record by mid-January, but their loss to Orlando was their season-worst third straight defeat. On January 27, 2018, he scored 37 points on 13-for-18 shooting with five 3-pointers in a 109–105 loss to the Golden State Warriors. On February 28, 2018, Irving helped the Celtics improve to 4–0 following the All-Star break with a 134–106 win over the Charlotte Hornets. Irving led Boston with 34 points, making 13 of 18 shots overall and going 4-for-6 from three-point range in the first three quarters. On March 24, 2018, he was ruled out for three to six weeks after undergoing a minimally-invasive procedure to remove a tension wire in his left knee. Less than two weeks later, he was ruled out for the entire postseason, with a recovery time of four to five months, after another procedure was scheduled to remove two screws from his patella that were inserted in 2015 to repair a fracture he suffered during that year's NBA Finals.
In February 2017, Irving stated in an interview for a podcast that he believes that the Earth is flat. In a later interview, he was less forceful in advancing his flat Earth belief, encouraging people to "do their own research" into the topic. In September 2017, Irving denied these claims and said that media misunderstood him as he was joking. However, in a June 2018 interview, when asked if he would admit that the world is round he said "I don't know. I really don't", and added that people should "do [their] own research for what [they] want to believe in" because "Our educational system is flawed." In October 2018, Irving apologized for his original flat Earth comments.