The Spurs have lost two in a row only twice this NBA season and are 9-1 on the second night of consecutive games.
Aldridge's three-point play with 52 seconds left gave the Spurs a 105-100 lead, and Parker made two free throws with 23 seconds remaining that bumped the lead to 107-101.
Two Aldridge free throws at the 3:55 mark and Leonard's baseline jumper with 3:34 to play gave San Antonio a 98-97 lead. Another Leonard basket stretched the lead to 100-97 with just under three minutes left.
Paul George scored a team-high 27 points for Indiana who dropped to 29-26 on the season.
San Antonio outrebounded Indiana 49-37.
Leonard and Patty Mills sank three-pointers in the third quarter's final 2:24, and the Spurs led 83-79 through 36 minutes. George had 12 third-quarter points to help the Pacers remain within striking distance.
The Pacers then surged to an 85-84 lead after beginning the fourth on a 6-1 run.
San Antonio outscored Indiana 21-12 to close the second quarter as the teams went into the half tied 49-49.
The Pacers hit 48.7 percent overall from the floor while the Spurs shot 46 percent.