Leading by three points at halftime, the Heat carried a 70-60 lead into the fourth quarter. Dragic scored nine points in the third. Miami led by as many as 27 points in the fourth quarter.
The Heat (13-13) shot 56.1 percent from the floor and went 14 of 27 from 3-point range, 51.9 percent.
Miami got 17 points from guard Josh Richardson and 14 points each off the bench from center Bam Adebayo and guard Tyler Johnson. Forward James Johnson chipped in 11 points, three assists, two steals and two blocks. Wayne Ellington scored 12 points, and Dion Waiters contributed 10.
"His aggressiveness was good tonight," Heat coach Erik Spoelstra said of Waiters. "He got some switches, bigs were on him, and he drove those right into the paint."
"The effort wasn't there," Bickerstaff said. "We didn't give the fans what they deserve tonight. It was disappointing to say the least."
While the Grizzlies' home record fell to 5-11, the Heat improved its road mark to 8-7 and, by winning in Memphis, closed a 2-1 trip.
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