Jimmy Hayes, Joe Morrow, Brett Connolly and Brad Marchand also scored for Boston, which had lost its first four homes games (0-3-1). Hayes, Loui Eriksson and Matt Beleskey each had two assists.
Mike Smith stopped 21 shots for the Coyotes, who played their fifth road game in eight days, finishing their trip at 2-2-1.
The Bruins also beat the Coyotes earlier this month, 5-3 in Arizona on Oct. 17.
Rask was barely tested in posting his 27th career shutout. He gave up 19 goals in Boston's first four home games.
The Bruins jumped ahead 1-0 late in the first period when Krejci came into the zone on the left wing during a 2-on-1 break and faked a backhand pass before slipping a forehand shot past Smith.
Krejci has a point in each of the first eight games. He also scored Boston's final goal in the last minute of the game.
They made it 2-0 early in the second. Beleskey fired a shot and Hayes banged home the rebound from the edge of the crease.
Morrow took a pass from Beleskey, spilt a pair of Coyotes' players at the blue line and unloaded a rising wrist shot that went over the left shoulder of Smith, making it 3-0 with 2:31 left in the second.
Connelly took a drop pass from Marchand and fired a wrister between Smith's pads midway into the third. Marchand added a power-play goal.
Arizona, playing its fifth game in eight days, seemed slow getting to the puck most of the game.
NOTES: Krejci's streak is the longest since Joe Juneau and Dmitri Kvartalnov did it in 14 in a row in 1992-93. . LW Beleskey was back in the lineup after missing the last two games with an upper body injury. . Arizona C Martin Hanzal, who had a league-leading 10 assists entering Tuesday, missed the game after sustaining a lower body injury in Monday's win at Toronto. . . Krejci's next assist will be his 300th. . Boston sent LW Max Talbot to Providence of the AHL. . Boston plays at Florida on Friday. The Coyotes open a three-game homestand Friday against Vancouver.