DALLAS (AP) — The Dallas Mavericks are on the brink of their first championship in the most fitting of ways: They cranked up their offense.

As much as coach Rick Carlisle preaches defense, this franchise that rose to prominence a decade ago by outscoring 'em did exactly that in Game 5 of the NBA finals, riding 29 points from Dirk Nowitzki and 13 3-pointers to a 112-103 victory over the Miami Heat on Thursday night for a 3-2 series lead.

The Mavs are headed to Miami looking to finish on Sunday night what they started in 2006. Dallas went there holding a 2-0 series lead, only to drop the next four games. This time, the Mavericks only need to win one of the last two to make Nowitzki, Jason Kidd and everyone else on the roster NBA champs for the first time.

"We're going in there Sunday swinging like we did today, from the jump," Nowitzki said.

Dallas players have been saying for days that they have yet to play their best game. They also had yet to play with the comfort of having the lead most of the night.

The Mavs did both this time.

"I said if we get to 100, we like our chances," Jason Terry said. "We did that."

The Mavericks hit the Heat with an offensive assault their vaunted defense simply couldn't stop.

Dallas posted the most points against Miami in a game, a half (60) and a quarter (30) this postseason.

The Mavs also had the best field-goal percentage (.565) and the most 3-pointers (13), and matched the most field goals (39) against the Heat in these playoffs.

And, to think, these guys had a .414 shooting percentage over the first four games of the series.

The reward for their improved aim was the comfort of playing from ahead most of the night.

Consider this difference: Dallas went from leading for a total of 35 minutes, 41 seconds over the first three games, to leading for 30:59 in this game alone, according to STATS, LLC.

"I thought in the first four games, we looked at the film, we stepped into good shots," Nowitzki said. "For some reason, we weren't knocking them down like we did in the first three series. If we had struggled like that in the first three series, I don't know if we would've gotten here. We talked about it, keeping stepping into shots when they are there. ... I thought we had big, timely shots tonight."

Four Mavericks had their most points of the series: Terry with 21, J.J. Barea with 17, Kidd with 13 and Brian Cardinal with four. Tyson Chandler matched his high with 13.

"My teammates get on me sometimes about shooting the ball and looking to score a little bit to help them," said Kidd, who was scoreless in Game 4. "Tonight was one of those games where I had some good looks and they went in."

As crisply as Dallas shot, leaky defense kept this from being a blowout.

Although the Mavericks were up by seven in the opening quarter, they came away trailing 31-30. They were ahead 60-57 at halftime and stretched it to 80-71, matching their biggest lead of the series, only to find themselves trailing 100-97 with 3:38 left.

That was nothing for a team that already had wiped out fourth-quarter deficits of 12 and nine points in its other wins.

So this veteran club responded the way it had all night, by hitting 3s.

Terry nailed the first, an open look from straightaway, to tie it at 100 with 3:23 left. After a dunk by Nowitzki put Dallas ahead — for good, as it turned out — Kidd started stretching the lead with a 3-pointer and Terry followed with another from the right side with 33.8 seconds left. He punctuated by his traditional flying jet pose in honor of his nickname and his initials: JET.

"We're a very resilient team, you know that," said Terry, who matched Nowitzki with eight points in the fourth quarter, even more impressive since he was often covered by LeBron James. "We've been in tough battles all playoffs long. It's not going to stop. It's going to get even harder. But we're ready. We're determined, and this is our time."

The Mavericks wound up closing the game on a 15-3 run. They became the first team this series to win consecutive games.

So, how did they treat the most significant win in franchise history?

Mildly, as they have all postseason.

Nowitzki put his arms up toward the bench, but hardly smiled. No, it wasn't the lingering effects of his sinus infection. It was the unfinished business of having 15 playoff wins, when they need 16.

After all, Boston held a 3-2 lead over the Lakers last year, only to blow it. Overall, 19 of the 26 teams that have led a finals 3-2 have gone on to be crowned champs, including Miami in '06.

"Hopefully I can enjoy it next week," Nowitzki said.

Fans certainly weren't subdued.

The 52nd and final home game this season was the most raucous yet, with repeated chants of "Beat the Heat" for the time all series. They also screamed "MVP" every chance they had for Nowitzki.

Now they're hoping for one more gathering at the American Airlines Center — with the Larry O'Brien Trophy.