The Spurs (41-12) were outrebounded 49-26, but compensated by scoring 29 points off 19 Chicago turnovers.
"One would hope that you could play with anybody in your system, but it was a tough challenge for them tonight," coach Gregg Popovich said. "And I couldn't be more proud of what they did."
San Antonio, 3-1 on its nine-game trip necessitated annually by the rodeo occupying the AT&T Center, has won six of seven away from home and has the league's best road record at 19-10.
Parker, who's averaged 30.3 points in his last three contests, sat out Monday with a swollen right knee to avoid playing back-to-back games. Duncan (knee) and Ginobili (hamstring) missed their fourth and fifth consecutive games, but all three are expected to play Wednesday.
Jackson is still out, and center Tiago Splitter could also find himself sidelined after an awkward fall in the first quarter Monday. He was icing his left ankle after the game.
"It's painful right now, but we'll see tomorrow how it feels," said Splitter, who had 16 points in 33 minutes.
The Spurs will try to piece it together again Wednesday against a Cavaliers team that's dropped two straight since a three-game winning streak. Cleveland (16-36) didn't fare well against another injury-hit club Monday, falling 100-92 to Minnesota.
The Cavs had their own injury scare when star guard Kyrie Irving rolled his ankle in the first half after landing on an opponent's foot. Irving hopped around painfully but played 36 minutes and scored 20 points. He wasn't available for interviews afterward as he spent time in the trainer's room.
Irving went 1 for 5 in the fourth quarter when the Timberwolves shot 75.0 percent and got 12 points from Luke Ridnour.
Wayne Ellington's 3-pointer cut the lead to 82-81 with 7:20 left, but Minnesota responded with a 10-2 run.
"We basically did it to ourselves," swingman C.J. Miles said. "They made some tough shots -- don't take anything away from them -- but for the most part, we gave the game to them.
"We just don't get it. It was just a poor effort from the start. It just didn't look like we were interested."
The Spurs won both meetings last season by a combined 51 points, shooting 57.0 percent from the field. Green averaged 16.5 points and hit seven of 11 3-pointers in the two games.
Irving averaged 16.0 points but shot 39.4 percent and had seven turnovers and eight assists.