SALT LAKE CITY -- James Harden claimed he had no clue that he missed his first 15 field goal attempts in Saturday's Game 3, the most consecutive misses from the floor in any game of his career. It certainly didn't impact the reigning MVP's confidence.

Harden scored 14 of his 22 points in the fourth quarter, hitting three of his last five field goal attempts, to help put the Houston Rockets on the brink of sweeping the Utah Jazz with a not-so-pretty 104-101 win.

"Keep shooting, keep being aggressive," said Harden, who finished 3-of-20 from the floor, 2-of-13 from 3-point range and 14-of-16 from the free throw line. "0-of-15, 14-of-15, 15-of-15, my job is to go out there and produce and be aggressive and in attack mode. Nothing changes."

Harden's 15 missed field goal attempts to begin the game were the most in the playoffs in the past 20 seasons, according to ESPN Stats & Information research. His first bucket didn't come until there was 7:34 remaining in the fourth quarter, and then Harden threw down a breakaway dunk.

On the next possession, Harden swished a step-back 3 from the "U" in the half-court logo, with his swagger certainly not sagging after he bricked his first nine 3-point attempts.

With the Rockets' lead down to one, Harden hit another step-back 3 with 1:11 remaining, providing a critical counterpunch during the Jazz's attempt to rally. Harden, who had 10 assists, was 4-for-4 from the line in the final two minutes to help Houston hold off Utah.

"Regardless of how you play during a game, you know that at the end of the game, that's James Harden," Jazz coach Quin Snyder said. "He's that good at the end. You give yourself a very small margin. With that said, I thought we laid it out there. I'm proud of how we played and how we competed. We just didn't get a win tonight to reflect that."

Harden, who won his second consecutive scoring title by averaging a career-best 36.1 points per game during the regular season, averaged 30.5 points during the Rockets' routs in the first two games of the series.

The Jazz, the second-ranked defense during the regular season, were humiliated by how Harden picked them apart in Houston and vowed to be more aggressive and competitive when the series shifted to Vivint Smart Home Arena in Salt Lake City.

"The way we started the game, we were tough," Jazz center Rudy Gobert said. "I don't think they felt us in the first two games. We should play that way every night. I think that's who we are, and we've got to play the same way every night."

Harden, however, declined to credit Utah's defense for his off shooting night. That's pretty much Harden's policy, as he prides himself on being a historically elite offensive force who consistently hits tough shots.

Asked if he noticed a higher level of intensity from the Jazz's defense, Harden smirked and said, "Nope, just missed a couple of shots. Two or three, I think."

Seated next to Harden at the podium, teammate Chris Paul cracked: "Gobert threw a couple of 'em, too."

Indeed, two of Gobert's seven blocks came at Harden's expense, and the reigning Defensive Player of the Year's presence was felt on some of Harden's other misses. The Jazz guards, primarily Ricky Rubio and Royce O'Neale, also did a better job of contesting Harden's shots than they did the previous two games.

"They played him tough, there's no doubt about it," Rockets coach Mike D'Antoni said. "They got into him, and they did what they were supposed to do, but James normally figures that stuff out anyway. So he just didn't have a great night -- and it happens."

Fortunately for the Rockets, Jazz star Donovan Mitchell also had an extended shooting drought, despite getting off to a spectacular start, and that allowed Houston to hang around even with Harden's off night.

Mitchell made five of his first six shots from the floor, including a spectacular alley-oop finish and an and-1 3-pointer during the Jazz's 8-0 run to open the game. But Mitchell, the only Utah player capable of creating his own shot on a consistent basis, missed 11 shots in a row at one point and finished with 34 points on 9-of-27 shooting.

"That's just my role, and I can't miss that many shots," said Mitchell, who is shooting 32.8 percent from the floor in the series. "I've got to be able to hit those, and we've got to capitalize."

Mitchell's final miss was an open 3-pointer behind a Gobert screen on the right wing that would have tied the game with 8.7 seconds remaining. The Jazz are 27-of-106 from 3-point range in the series.

Rockets power forward PJ Tucker grabbed the rebound of Mitchell's final miss and swished the dagger free throws. It was a fitting finish after Tucker grabbed a crucial offensive rebound in traffic on the Rockets' previous possession.

For much of the Rockets' season, Harden carried his team with his historic scoring feats. This victory served as proof that Houston can find a way to win even when its superstar has a rough night.

"I didn't shoot the ball well, and we still won," Harden said. "Guys stepped up major tonight, and that's what we're going to need."