The Jazz ended up being outscored 22-2 to finish the half, after fighting their way back to within 31-26 with 7:04 remaining after a 9-0 run.
They actually had a chance to cut further into the lead, but after Jamaal Tinsley's steal, DeMarre Carroll was called for a charging foul. It all crumbled quickly after that. The Jazz missed 12 shots in a row, with Alec Burks, Al Jefferson and Josh Howard each going 0-for-3, while Millsap was 0-for-2 and Gordon Hayward missed his only attempt.
The Spurs took advantage with a 20-0 run, halted only by Millsap's jumper.
"We had [good] looks, we had layups not go in," Millsap said. "When that happens, you kind of get down on yourself."
Jazz coach Tyrone Corbin replaced Derrick Favors with Al Jefferson just before the disastrous stretch. Favors had played nine consecutive minutes and spurred the Jazz's rally, although he made only 2 of 7 shots.
The Spurs' Tony Parker and Tim Duncan also re-entered the game just before the big run. So did guard Danny Green, who had as much to do with San Antonio's success as any of the Big Three. Green scored 11 points during the 20-0 run.
Corbin said his team must learn in the playoffs to "make sure you take care of the little parts of the game and cut off runs soon."
Corbin used one timeout during the spurt, after San Antonio had scored 11 straight points.