Coming off a first half when he went 1 for 4 from the floor, Duncan scored 11 points on 4-of-9 shooting in the third to help San Antonio open a 71-66 lead after three.
"I started out the second half the exact same way and finally got some to fall," he said. "They kept coming to me and I just put it in the hole. There wasn't anything I changed, anything I saw."
Boris Diaw added 18 points and Duncan grabbed nine rebounds to lead the Spurs to their fifth win in seven games.
"He's had that same demeanor since Day 1 when he arrived," Popovich said of Duncan. "He doesn't get excited about wins. He doesn't get down about losses. He just loves to compete and he keeps a real steady attitude, which everybody kind of feeds off in a way."
First-year Boston coach Brad Stevens thought Duncan decided to take command more after halftime.
"He changed," Stevens said. "I mean, he went back to being really aggressive on the blocks. I thought in the first half we did a really good job on a couple of catches that he did have down on the block, but he kind of put (them) on his shoulders. He wasn't going to be denied -- and we don't have great matchups for him. There's not many great matchups for him in the NBA or in the world."
Duncan scored 12 points and was 5 of 6 from the floor in the fourth.
"He is arguably one of the best power forwards of all time, and he's doing it at 38," Humphries said.
Boston was minus guard Avery Bradley, who was sidelined with a sprained right ankle.
After the Celtics scored the first points of the fourth quarter on a jumper by Humphries, San Antonio went on a 12-4 run. The Spurs went 6 of 8 to start the period, keyed by Danny Green's 3 from the left corner that made it 79-70 with just under 10 minutes to play.
After a foul-line jumper by Humphries, Duncan had consecutive baskets, the second a jumper that pushed the Spurs' lead to 85-74 with 8:06 left.
San Antonio broke it open with a 11-0 run midway into the quarter that was capped by Belinelli's 3-pointer with 4 minutes left.
The Spurs used a 9-2 run late in the third and opened their five-point lead heading into the fourth.
Duncan didn't score his first points until a basket late in the first half.
The Celtics went on a 12-0 run, bridging the end of the first quarter and the start of the second to pull to their first lead of the game, 26-25, on Phil Pressey's 3-pointer.
San Antonio led 48-44 at halftime.
Stevens said Bradley re-sprained the ankle that cost him five games at the end of January. Stevens said he could be out after the All-Star break. ... Before the game, Stevens praised the Spurs' ability to overcome the loss of players due to injuries. "I think some of the most inspiring basketball I've ever watched is when they don't have all their players," he said. ... The Spurs played their sixth game of a nine-game road trip that will carry over the break with the final three. Boston opens the post-break schedule with a four-game trip, starting against Phoenix next Wednesday. ... Hall of Famer Bill Russell turned 80 Wednesday. ... San Antonio beat Boston at home on Nov. 20, 104-93 in the only other meeting this season. ... Ginobili has a tight left hamstring and missed his eighth straight. Splitter was out for his third consecutive because of a bruised right shin and Parker was sidelined with lower back tightness. ... Stevens said Boston F Jared Sullinger played just 18 1/2 minutes because he was "sick."
MVP: Tim Duncan had just two points at halftime as the Spurs struggled without Tony Parker. The 37-year-old then erupted for 23 second-half points, and San Antonio won its final pre-All-Star contest 104-92 to head into the break on a good note.
X factor: Marco Belinelli was all over the place. One of the newest Spurs nearly registered a triple-double with 16 points, 11 rebounds and eight assists, and he hit a couple of 3-pointers as he warms up for the 3-point contest this weekend in New Orleans.
That was ... much-needed. The Spurs have been dealing with pretty substantial injury issues, basically since the calendar switched to the new year. They didn't have Kawhi Leonard, Manu Ginobili, Parker or Tiago Splitter against the Celtics, so needless to say, a win with so many injured players is an important one.