Patty Mills came off the bench to score 29 points, Marco Belinelli hit a go-ahead 3-pointer with 1:34 remaining and San Antonio rallied in the second half to pull out a 111-109 victory against the Trail Blazers.
San Antonio has won two of three games this season when Duncan and Parker were both absent from the lineup.
Mills helped fill the void with a 24-point second half. The fourth-year guard from Australia came off the bench to hit 13 of 26 shots against the Blazers.
Belinelli had 20 points and Manu Ginobili 16 for San Antonio.
Mills has been on a hot streak since the All-Star break concluded, scoring 25 and 29 points in the Spurs' first two games back.
"If it wasn't for him the last couple nights, we would have really struggled," San Antonio forward Danny Green said. "He's doing what Tony usually does, in taking over in that fourth quarter."
Mills explained his recent stretch in humble tones, saying "for me, it's just been learning from great guys. We've got three future Hall of Famers and a great coach, so I've just sat back and learned."
It wasn't just Mills, though. Belinelli hit four 3-pointers, and Tiago Splitter had 15 points and six rebounds in returning to the lineup for the first time since Feb. 6.
"I thought the effort was fantastic," Spurs coach Gregg Popovich said.
Portland was without leading scorer and rebounder LaMarcus Aldridge, who missed the game with a groin injury and is expected to be out at least a week. Also sidelined were forward Joel Freeland (knee) and center Meyers Leonard (ankle).
Aside from Duncan and Parker, the Spurs also were without guard Kawhi Leonard (right hand).
Damian Lillard scored 31 points, including 15 during the fourth quarter, for Portland. Coming off his first All-Star Game appearance, Lillard hit 13 of 21 shots and handed out six assists.
Without Aldridge, Freeland and Leonard, the Blazers had to resort to playing a small lineup. It resulted in erratic play, with stretches when the Blazers' offense went missing.
"We tried to beat San Antonio at their game and they did it better than us," Portland coach Terry Stotts said. "San Antonio is used to playing these games without their guys and they plug guys in and they play well."
Trailing 81-79 after three quarters, San Antonio took command when Green hit back-to-back 3-pointers to fuel a 10-0 run at the fourth quarter's outset. The Spurs led by as many as 10 points, but the Blazers eventually pulled even at 101 on Matthews' steal and dunk with 1:52 remaining.
On San Antonio's next possession, Belinelli hit a 3-pointer from the top of the key with 1:34 left to put the Spurs back on top.
Portland led by as many as eight points during the first half, and settled for a 52-51 halftime lead.
Both teams had big runs during a free-flowing third quarter. Mills finished an 8-2 run with a layup to give San Antonio a 69-61 lead. Portland responded with seven consecutive points, then took a 79-75 lead when Williams scored six consecutive points late in the quarter.
Portland was the last NBA team to use the same starting lineup this season until Wednesday, when Dorell Wright replaced Aldridge against San Antonio. The Blazers are the first team since the 2010-11 Spurs to start the same lineup during its first 53 games. ... Splitter returned to the lineup after missing the past four games with a calf injury. ... Blazers' forward Victor Claver, who hasn't played since Nov. 15 and has logged just three minutes of playing time this season, made a first-quarter appearance and played seven minutes. San Antonio concludes a nine-game road trip that began Feb. 3 on Friday at Phoenix. ... San Antonio was 1-9 in its previous 10 games at Portland.