Earlier this season, the team played a stretch of 22 straight games without Manu Ginobili, and San Antonio lost backup point guard T.J. Ford to an injury-related retirement earlier this month.
Parker left with a left hamstring strain with 8:03 remaining in the second quarter. He spoke briefly with Spurs coach Gregg Popovich before heading to the locker room with two points and six assists.
"I think they said mild hamstring, so we won't know much until tomorrow," Popovich said. "Not good timing."
Stephen Jackson and Gary Neal showed they can step up if needed, scoring 16 points for the Spurs (30-14), who won their fourth straight game and fifth in their last six. Minnesota was playing catch-up the entire game after trailing 32-16 following the first quarter.
"Things are going to be difficult for a minute until we figure it out without Tony," Jackson said. "He's the head to our monster, but at the same time, we're in a good position when we have Ginobili being able to play point, be able to move the ball. We just have to figure it out. Gary and Ginobili did a great job of picking up the slack."
Kevin Love had 17 points and 12 rebounds for his league-leading 40th double-double, but Minnesota (23-25) lost for the fourth time in six games to fall further behind in the Western Conference playoff race.
With Parker out, Neal is the primary backup point guard. The team sent rookie point guard Cory Joseph to the Austin Toros of the NBA D-League on Tuesday.
"Gary did a great job (at point guard) for a 2-guard," Popovich said. "He's not a 1, but he kind of likes it for some strange reason. So we're happy he can do what he does at that position. Manu does a little bit, so the two of them share it."
Minnesota had won the previous two games in the season series, which concluded Wednesday. The first victory snapped a 16-game skid for the Timberwolves in San Antonio, while Ginobili broke his left hand in the second game.
Duncan, though, made sure there was no series sweep.
"Tim's been really fresh all year long," Popovich said. "I'm really enthused about his health, his body, the way he's been taking care of himself. He's got quickness and he's got more agility than he's had in a while. He's had it for the whole season. It's been fun to watch."
The Timberwolves were playing without starting center Nikola Pekovic, their second-leading scorer and rebounder. The second-year big man went back to Minnesota before the game to have his sore left ankle examined. He also will miss Friday's game at Oklahoma City, which ends the team's seven-game road trip.
"Pek is huge for us," Love said. "He's the guy we can throw it into and know we can get easy buckets. He can keep the other team off the glass. It was tough for us."
Daniel Green had 14 points and seven rebounds for the Spurs, who outrebounded the Timberwolves 56-41. San Antonio had 17 offensive rebounds.
"As a group they did a good job on the offensive boards," Love said. "They had three days' rest, and we seemed to not have any legs, me included."
With Pekovic out, Minnesota went with a smaller lineup, starting Love at center. Before the game, Minnesota coach Rick Adelman was blunt in his assessment of the team's other likely option, starting Darko Milicic at center.
"He hasn't done anything to give you faith that he's going to go out and do the job," Adelman said before the game. "He's gotten himself out of shape, and I don't think he's been as driven as you'd like."
Milicic didn't play.
The Spurs retired Bruce Bowen's No. 12 after the game. Bowen was on the league's All-Defensive team eight times and started on the Spurs' championship teams in 2003, 2005 and 2007. ... Spurs F Matt Bonner missed the game with back spasms. "He just came up tight yesterday in practice," Popovich said. "I don't think it's anything real serious, but we don't want to take any chances with him." ... Timberwolves F Michael Beasley, who has been battling a sprained left big toe, didn't play in the second half.