A 14-2 run that included a pair of 3-pointers by Green midway through the fourth finally allowed the Spurs to take control. Before the run, San Antonio appeared sluggish and unable to pull away from the Magic, who were within four points at 74-70 with 10:37 remaining.
Already without Manu Ginobili, the Spurs rested Tony Parker and Kawhi Leonard, and used Tim Duncan for only 14 minutes.
Maurice Harkless scored 18 points for Orlando. The Magic kept it close by taking advantage of nine first-half turnovers by the Spurs and 16 overall. Nikola Vucevic added 16 points and 14 rebounds, and Beno Udrih scored 14.
The Spurs avoided their first three-game losing streak since 2011 and got the much-needed victory after deflating losses in their last two outings. Chris Bosh's 3-pointer with 1.1 seconds on Sunday gave Miami an 88-86 victory and Mike Conley scored a go-ahead layup with 0.6 seconds left, giving Memphis a 92-90 win.
The Spurs went as deep as they could into the bench, calling on little-used big man Aaron Baynes, who entered the game late in the third and scored four quick points to spark a mini-run that gave San Antonio a 73-65 lead going into the fourth.
San Antonio already was playing without four players due to various injuries when forward Stephen Jackson tweaked his right foot three minutes into the game. The scare was short-lived and Jackson stayed in the game.
Leonard was sidelined for a second straight game with a sore left knee and Parker sat out to give his left ankle some rest. He missed eight games after spraining the ankle on Feb. 27 against Sacramento and had played in the previous five games before missing Wednesday's contest.
Duncan scored five points as Spurs coach Gregg Popovich rested most of his regular starters.
San Antonio jumped out to a quick 10-point lead in the opening period, before the Magic buckled down and recorded six blocks in the quarter that sparked a 17-7 run to tie the game at 21.
The Spurs travel to Oklahoma City for a Western Conference showdown Thursday after extending their lead to 1 1/2 games over the idle Thunder.