HOUSTON -- The owner wearing the cool sunglasses slowly got up from his courtside seat as the standing ovation began.

Leslie Alexander, who owns the Houston Rockets, shook hands with some people sitting next to him as if he's been here before.

Well, he has. It's just that this Rockets version of the big three as a group hadn't escaped the first round until Tuesday night.

The Rockets eliminated the Dallas Mavericks in five games with a 103-94 victory on Tuesday, earning a berth in the second round for just the second time since 1997.

The Rockets' big three of Kevin McHale, the coach, James Harden, the MVP candidate, and Dwight Howard, the star center, advanced after being knocked out in the first round in each of the past two seasons. Howard has been around since the 2013-14 season.

"I wish we could have McHale out there playing, too," a smiling Rockets general manager Daryl Morey told ESPN.com after the game. "James and Dwight came up big tonight. If we're going to win and go as far as we want, and we've got great players around them, it's going to come down to James and Dwight executing, and they did it tonight."

After a grueling 2014-15 season, in which they lost 180 combined games to injuries, the Rockets won a Southwest Division title, secured a No. 2 seed and advanced into the second round.

"We have a lot of guys in this locker room that are hungry," Harden said. "They want to win and want to do whatever it takes to win. When you get a group like that, you got a lot of guys who are willing to sacrifice."

McHale hasn't coached a team into the second round and hasn't been there since his Hall of Fame playing career. His two seasons in Minnesota are tough to count since he never had a full season to fix things. The past two seasons with Harden and Howard ended in playoff agony.

"Eventually, if you hang around long enough, it happens to everybody," McHale said. "It was a crazy year, all year long, and you saw all the different injuries, and I talked about that when we won the division that night. Guys just kept on grinding away."

Howard and Harden led the way in the Game 5 clincher. Howard posted 18 points and 19 rebounds, his ninth double-double in 11 playoff games with the Rockets. He altered shots -- blocking four -- and continued to be a physical presence and maintain calm after picking up two quick fouls in the opening quarter.

Harden was an excellent playmaker again, scoring a game-high 28 points to go along with eight assists. He was 6 for 6 from the free-throw line.

Harden just made big plays, like a steal of a Dirk Nowitzki pass to the corner that set up a drive and dish to Terrence Jones, whose dunk pushed the home team to a 99-91 lead with 69 seconds to play. On the next possession, Harden found Jones again for another dunk, extending the lead to 101-91 and sending the crowd into a frenzy.

Of course, McHale had a hand in this, sticking with point guard Pablo Prigioni for critical fourth-quarter minutes and playing Jones in the final frame after sitting him for the last 20 minutes of Game 4.

Jones finished with 15 points and five rebounds, including 10 in the fourth.

Josh Smith, who was thought to be a problem child in Detroit, is not only an upstanding citizen but a trusted member of this team under McHale.

Smith produced a 20-point, eight-rebound night. And while he struggles at the foul line, shooting 43.5 percent, he made 4 of 8 in Game 5, forcing Mavs coach Rick Carlisle to stop using the Hack-a-Shaq strategy.

These Rockets players act like the past two seasons never happened, and that's probably the best way to approach things, given how Morey has radically changed the roster. McHale has the players believing that there's nothing to gain from looking behind, because it would only distract them from the bigger goal.

And now as the Rockets advance, this trio of McHale, Harden and Howard are hopeful they can give Alexander something he hasn't seen since 1995 -- a championship trophy, or at least a legit chance at one.

"We have to stay humble," Howard said. "Anything can happen. We have to be thankful for being in this position. We can't take it for granted. So for me and everybody else, we have to continue to work and continue to get in the gym and get better and stay hungry."