The Houston Rockets have imposed their will against the Jazz. They have a 3-1 Western Conference semifinals series lead heading into Tuesday night’s Game 5 at the Toyota Center. A trip to the Western Conference finals and showdown against the Golden State Warriors seems like a formality.

And the Rockets aren’t satisfied.

It’s easy for them not to be. In addition to building an almost perfect roster to contend for a title, Rockets General Manager Daryl Money built a roster that largely hasn’t experienced ultimate success.

Small forward Trevor Ariza is the only Houston starter who has won an NBA title, and he was a young reserve with the Kobe Bryant-led Los Angeles Lakers almost a decade ago. James Harden and Chris Paul? They’ve been criticized their entire careers for not winning enough. Head coach Mike D’Antoni? He once took the Phoenix Suns to the Western Conference finals, but was thwarted by Tim Duncan and the San Antonio Spurs.

The Rockets are hungry, which spells trouble for a young an inexperienced Jazz team. Their main guys know what it’s like to go through postseason failure. And while they hope this season is their turn, they know they have to go out and prove it.

“We’re not satisfied with just being up 3-1,” Harden said. “At the start of training camp, the beginning of the regular season and this entire post season, we didn’t come thing far just to be up 3-1 in the semifinals. We’ve got a long way to go.”

In the moments following Game 4, Paul recounted in an interview of what it was like the last time he led a team to a 3-1 Western Conference semifinals series lead. His Los Angeles Clippers promptly lost three consecutive games to the Houston Rockets.

“It went bad real quick,” Paul said.

Throughout the postseason, Rockets veterans have spoken and emphasized living in the moment and taking advantage of the opportunity before them. Indeed, Clint Capela, 23, is the only Houston rotation player under the age of 25. Harden is in his prime. Paul and PJ Tucker are 33. Ariza is 32, as is Gerald Green. Eric Gordon is 29.

So, for this Rockets core, a title chase this season represents the best chance at a championship many of them have had in their careers. They fully intend on trying to make the most of it.

“That’s exactly what it was,” D’Antoni said. “They [the Jazz] came out with a lot of energy and getting into us and really we couldn’t even run a set because they were so into it. The ball couldn’t move. Thank gosh we have two of the best iso guys and we kind of went into that. It was hard fought.”

Houston played Sunday night with the urgency of a team trailing in a series, not one that looked to be in control after a blowout win in Game 3. The Rockets defended staunchly on every possession. Capela was all over the place, recording 12 points and 15 rebounds while blocking six shots. Harden and Paul were maestro’s delivering on every play offensively, keeping the Jazz at bay with clutch shots down the stretch.

The Rockets played like a team that knows playoff failure, a team that knows they have to keep their foot on the pedal. They weren’t satisfied with a road split at Vivint Smart Home Arena. They were intent on the sweep.

And, now, they are on the verge of moving on to the matchup everyone has been anticipating for months: A series with the Warriors.

“We knew they were going to come out more aggressive, and they did,” Harden said. “We kept our composure and got shots that we needed. As long as we got a good shot and our defense went back to set up, that’s all we can ask for.”