The Pacers scored the first six points of overtime before Houston scored the next six to tie it at 99 with about 2 minutes left.
Monta Ellis made two baskets after that to put the Pacers up twice, but each time Houston responded with a 3-pointer. Ariza hit the first one and Brewer made the second to make it 105-103 with 40.9 seconds left.
Ariza added a dunk with 2 seconds left to secure Houston's third straight victory.
The Rockets trailed by 12 midway through the fourth quarter before rallying to tie it with 17.1 seconds left on a 3 by Ariza. The Pacers had a chance to win in regulation, but Ellis missed a jump shot at the buzzer.
Paul George had just four points in the first half before scoring 14 of his 20 in a 27-point third quarter to help Indiana build a big lead before Houston came back in the fourth.
James Harden had 21 points and Dwight Howard added 21 points and 17 rebounds for his fifth straight double-double in his return after missing Thursday's game with soreness in his lower back.
The Pacers' lead was 12 before the Rockets used a 12-1 run to get to 89-88 with about 3 minutes left.
The Pacers had a 13-point lead entering the fourth and were up by 12 after a one-handed dunk by Jordan Hill with about 6 1/2 minutes left.
Indiana led by three at halftime and scored the first five points of the second half to make it 55-48. Houston got a 3-pointer from Patrick Beverley followed by a hook shot from Howard to get within two, but Indiana padded the lead with a 14-6 spurt to make it 69-59.
George made two 3-pointers in that span, and Lavoy Allen and Ian Mahinmi added four points each for the Pacers. The Rockets scored all their points in that stretch on free throws as they went almost 6 minutes without a field goal.
Harden finally ended the drought with a layup with less than 3 minutes left in the third. He made a 3-pointer after a dunk by George to cut the lead to 71-64.
George wasn't done with his work in the quarter as that dunk was the first of eight straight points he scored to end the period and make it 77-64. The stretch was highlighted by his last points in the third when he made an off-balance jumper as he was fouled by Harden and hit the free throw.
The Pacers trailed by four in the second quarter before using an 11-2 run to take a 50-45 lead just before halftime. Harden hit a 3-pointer just before the quarter ended to cut it to 50-48 at halftime.
Pacers: Indiana had 18 turnovers after committing a season-high 25 in its previous game. ... Ellis had a season-high 13 assists.
Rockets: G Ty Lawson served the second of a three-game suspension for driving under the influence last July. ... F/C Donatas Motiejunas missed his fourth straight game with back soreness. ... C Clint Capela had three steals to give him at least three in two straight games after doing so only twice in his first 35 games this season.