After Indiana elected not to make Turner an $8.7 million qualifying offer, he became an unrestricted free agent. According to his agent, Turner agreed to sign with the Boston Celtics on July 21, 2014. He officially signed with the Celtics on September 29, 2014. He began the season as a reserve, but when Marcus Smart and Rajon Rondo endured concurrent injuries, Turner scored a team-high 19 points in a starting role in a win against the Chicago Bulls. On December 8, 2014, against the Washington Wizards, Turner forced overtime by sinking a three-point shot with 0.9 seconds left in regulation, but missed a 20-foot (6.1 m) jump shot with 0.9 seconds remaining in the second overtime which would have given the Celtics the lead. When he was inserted into the starting lineup at point guard on December 31, 2014, against the Sacramento Kings, he posted a double double with 11 assists and 10 points. Chicago native Turner posted a season-high 29 points at the United Center against the Chicago Bulls on January 3. Turner hit his fourth (in eight attempts) career last second game winning shot with a three-pointer with 1.9 seconds left as his team trailed 89–87 against the Portland Trail Blazers on January 22, 2015. Then on February 11, 2015, he hit a game winner with 0.2 seconds left against Atlanta Hawks. Evan Turner posted his first career triple double on February 25, 2015, against the New York Knicks with 10 points, 10 assists and 12 rebounds. On March 13, 2015, Turner scored 24 of his season-high 30 points in the second half, including 16 in the fourth quarter to help the Celtics rally past the Orlando Magic. He posted two more triple doubles on March 23 against the Brooklyn Nets (19 points, 10 rebounds, and 12 assists) and on April 1 against the Indiana Pacers (13 points, 11 rebounds, and 12 assists). On April 10, he recorded a career-high 13 assists against the Cleveland Cavaliers. Turner played every game in the 2014–15 season and finished with averages of 9.5 points, 5.1 rebounds, and a career-high 5.5 assists per game. During the offseason, he was named as a participant in the first-ever NBA Africa Game.