Collison added eight assists, made all 12 of his foul shots and connected on 8 of 13 from the field, including 2 of 4 from outside the arc.
Memphis lost its third straight. It had a chance to tie it after a review of an out-of-bounds call gave the Grizzlies the ball with 9 seconds left. Marc Gasol's 3-pointer with 3 seconds remaining was off the mark.
Gasol led Memphis with 35 points and 13 rebounds. Tyreke Evans added 18 points and nine assists, while Chandler Parsons scored 13 points.
Bojan Bogdanovic finished with 16 points for Indiana, including a 3-pointer that momentarily stalled a fourth-quarter surge by Memphis.
The Grizzlies trailed by 17 early in the fourth but scored 10 straight points to cut the deficit to 105-98 before Bogdanovic's 3.
Memphis played without starting point guard Mike Conley, who has a sore left Achilles tendon. Despite shooting well at times, Memphis' offense seemed in disarray and committed fifteen turnovers.