Cousins went to the bench with four fouls early in the third quarter and the Kings trailing 59-47. But Sacramento rallied without its leading scorer, using a 15-4 run to briefly grab the lead.
Cousins finally got going in the final period, challenging Duncan inside and scoring five straight Kings points during one stretch to keep Sacramento close.
"That was a competitive, big man battle," Cousins said. "I have the upmost respect for Tim Duncan. He's the greatest forward that the NBA has."
Duncan, who had eight points in the fourth, was 9 for 12 from the field for the game and finished with four assists and three steals.
Duncan was clearly looking for shots early. He made the Spurs' first basket on a jumper and had 12 points and seven rebounds at the break.
"I'll be there for whatever (plays) are called for me on any given night," Duncan said. "Nights where I'm playing well he (Popovich) will run plays through me."
Tyreke Evans scored eight points and both Thompson and Thornton had seven in the third quarter, helping the Kings close to 69-68 heading into the fourth. The Spurs shot 7 of 20 in the third after shooting nearly 55 percent in the first half.
After an impressive opening quarter, the Kings shot 25 percent in the second period and were outscored 23-12. Thompson had 10 first-half points.
NOTES: Kings reserve PG Aaron Brooks missed all five shots and went scoreless in 19 minutes. ... Kings rookie Thomas Robinson was held out for the first game in a two-game suspension for elbowing Detroit forward Jonas Jerebko. ... Veteran John Salmons, who missed much of the preseason due to his wife's pregnancy, played his first game of the season for the Kings. He had one points in five fourth-quarter minutes.