HOUSTON (AP) — After advancing to the second round of the NBA playoffs for the first time since 2009, the Houston Rockets shifted their focus to much bigger goals.

They’re looking to become the first Houston team to win a Western Conference semifinal since 1997.

“Everybody is locked in on what our goal is and that’s to win a championship,” said Dwight Howard, who had 18 points and 19 rebounds to help the Rockets dominate inside in beating the Dallas Mavericks 103-94 on Tuesday night to make it past the first round.

James Harden scored 28, Terrence Jones had 10 of his 15 points in the fourth quarter, and the Rockets xorcised any bad feelings that lingered from last year’s opening-round loss to Portland.

Houston took the Western Conference series 4-1 to advance to face the winner of the Clippers-Spurs series, which San Antonio leads 3-2.

“We are going to peak at the right time and you get hot because you’ve only got to win 16 games and we’ve won four of those,” Jason Terry said. “So, we are a quarter of the way home.”

The Rockets bounced back from a lackluster performance in a 121-109 loss in Game 4 to head to the West semifinals for the first time since Yao Ming starred for Houston.

Harden said the key will be to not rest on what they’ve already done.

“We’re going to act like we’ve been here before,” he said. “We’re going to enjoy (Tuesday) and stay humble about it ... and be ready to go and give it our all.”

The victory meant a little more to Howard, who missed half of Houston’s regular-season games with injuries.

“There are times when I get super emotional because I want to win,” Howard said. “I don’t want to be sitting at home watching somebody else holding up the trophy. Minutes, fouls, missed free throws or whatever it may be, I’m going to stay locked in on what the task is and that’s to win the game.”

The Mavericks couldn’t get going from long-range, going just 5 of 26 on 3-pointers.

Monta Ellis led Dallas with 25 points and Dirk Nowitzki added 22.

The Mavericks didn’t lead after early in the first quarter, but a 7-0 run, capped by a basket by J.J. Barea, got them within three with about 5 minutes remaining. Then Jones took over, making a three-point play followed by a corner 3 to push it to 94-85.

Dallas scored the next four points before Harden swished a 3-pointer under heavy pressure to make it 97-89 with 2 1/2 minutes left.

Harden grabbed a steal soon after that and made a no-look pass to Jones, who dunked it, eliciting chants of “MVP! MVP!” from the crowd.

Houston’s next basket came when Harden tossed a long pass to Jones for another slam to make it 101-91 with less than a minute left.

Al-Farouq Aminu and J.J. Barea were the unlikely stars that helped the Mavericks avoid elimination in Game 4. Aminu had 14 points before fouling out in the fourth, but Barea was largely ineffective, finishing with six points and three turnovers. Nowitzki led Dallas with 14 rebounds, but Tyson Chandler had just six.

Howard struggled offensively early in the fourth quarter and had missed two straight shots when he provided a defensive highlight by blocking a shot by Barea into the stands.

Dallas used the Hack-A-Howard tactic to try and slow Houston down in the third quarter, fouling him intentionally four times. Howard made half of the free throws, but the Mavericks couldn’t make many plays on the other end.

Smith and Harden carried the Rockets early, scoring 16 points apiece in the first half. Nowitzki got off to a terrible start, going 2 of 11 before halftime and the Mavericks made just 1 of 13 3-point attempts in the first half.

The Mavericks started intentionally fouling Smith late in the half and he made two of four free throws. But the second miss worked out for the Rockets anyway, when Clint Capela grabbed a rebound and dished it to Harden, who made a 3-pointer to leave Houston up 56-50 at halftime.