Phoenix (8-16) had cut a late eight-point deficit down to two when Irving calmly drained a 3-pointer with 1:53 left to start a crazy finish that saw the home team hold on for the win, despite 38 points from Devin Booker.
Booker, who scored 70 the last time he played at TD Garden, 51 in the second half, fouled out Saturday after hitting a 3-pointer to bring his team to within three with 17.6 seconds left.
Marcus Smart hit four straight free throws to help put the game on ice for Boston (20-4).
The win was the 10th in the last 11 home games for the Celtics, 20-2 in their last 22 games overall.
The Celtics, playing the second game of a four-game homestand, used an 18-2 run bridging the third and fourth quarters to take control of the game, but the feisty Suns battled back.
Jaylen Brown and Marcus Morris scored 17 points apiece, while Jayson Tatum had 15 points and six rebounds. Al Horford had 14 points, a career-high 11 assists and five rebounds. Smart added 13 points, seven assists and seven rebounds off the bench. Irving had five of Boston's 32 assists (on 42 baskets).
T.J. Warren scored 19 points and veteran big man Tyson Chandler delivered a season-high 18 rebounds and 14 points in the loss for Phoenix.
NOTES: Phoenix C Alex Len, averaging 8.9 points and 9.4 rebounds per game off the bench, was out with an ankle injury. ... Phoenix interim coach Jay Troiano on Boston counterpart Brad Stevens: "He was one of the first coaches to text (me) when I got the opportunity here. We're on a board of directors here in Boston for a program called 'Shooting Touch.' " ... Suns rookie F Josh Jackson said a misunderstanding between him and his agent led to snubbing Celtics president Danny Ainge for a workout in Sacramento. "The day they were supposed to come in I wasn't aware, and wasn't prepared," he said. "So I'm not going to work out if I'm not prepared." He heard boos during the game. ... The Suns continue their road trip at Philadelphia Monday while the Celtics wrap up their three-game season series with the Milwaukee Bucks the same night.