Cousins had the final five points during Sacramento's surge, including ripping a rebound away from rookie Festus Ezeli and drawing a foul to start a three-point play.
"I've started the season off pretty rough," Cousins said. "I know the way I play affects this team in a lot of ways. I knew I had to step up tonight."
Seemed everybody on Sacramento's side did.
Smart's nifty move in the second quarter came during his team's first-half spurt. And in separate second-half incidents, three more pieces of plastic fell down from the scoreboard hanging above center court. Some fans even chanted "New Arena!"
The Kings almost crumbled on the court, too.
Curry made a 3-pointer and Thompson converted a layup through traffic with a little more than 2 minutes remaining to bring the Warriors within three. Thompson's two free throws sliced Sacramento's lead to 93-92 with 31.3 seconds left.
After Cousins missed a difficult running shot, Golden State called timeout with 10.3 seconds remaining. Thompson then missed a contested shot near the free-throw line, James Johnson grabbed the rebound and was fouled.
Johnson missed the second free throw to give the Warriors another chance with 1.3 seconds to play. Off the in-bound play, Curry missed a 3-pointer over big man Chuck Hayes as time expired.
"I thought it was in," Hayes said. "When Klay Thompson shot the other one, I thought it was good. Those are two guys when the ball leaves their hands, you think it's good."
Golden State was trying to start 3-0 on the road for the first time since 1994-95, when it won at San Antonio, Denver and Utah. The Warriors won at Phoenix and the Los Angeles Clippers already this season while losing their only home game to Memphis.
The Kings haven't started 0-4 since 2008. All four of those games were on the road that season, when Sacramento finished with an NBA-worst 17-65 record.
NOTES: Thompson played through a toothache. ... Sacramento Mayor Kevin Johnson chatted with players from both teams from his courtside seat during pregame warmups.
Antonio Gonzalez can be reached at: www.twitter.com/agonzalezAP