The Dallas Mavericks ended three decades of frustration by capturing their first championship with a 105-95 victory over the Miami Heat on Sunday to win the best-of-seven NBA Finals 4-2.

Veteran guard Jason Terry came off the bench to score 27 points and lead a long-range assault by the Mavericks, who connected on 11 of 26 from beyond the arc.

"This team never gave up when faced with adversity -- always responded," said a jubilant Terry.

LeBron James had nine points in the opening period but finished with only 21 for the game to lead the Heat.

Chris Bosh scored 19 and Mario Chalmers added 18 for Miami, who had 16 turnovers and hit only seven of 23 from three-point range and only 20 of 33 from the line.

"I just can't believe the journey," said 17-year NBA guard Jason Kidd of the Mavericks. "I came here twice (the finals) and this is the third time. The third time is the charm."

Dallas forward Dirk Nowitzki, the MVP of the series, had an off-night, scoring 21 points but shooting only nine of 27 from the floor.

However, the 32-year-old, 10-time All-Star had 10 points in the fourth quarter to squash Miami's comeback attempts and claim his first title.

"I still really can't believe it," said Nowitzki. "We worked so hard and so long for it.

"The team has been on an unbelievable ride through so many ups and downs and always staying together and working. I still can't believe it."

"To our fans who came here to Miami ... We heard you," Mavericks owner Mark Cuban told the crowd after the game. "You rock."

Nowitzki shot one for 12 from the floor in the first half but Dallas still held a 53-51 lead because of 19 points by Terry, who hit eight of 10 shots, including three of five from beyond the arc.

Dallas, buoyed by eight points from Nowitzki and six from Jason Kidd, outscored the Heat 28-21 in the third quarter to take an 81-72 lead into the final frame.

Six-foot guard J.J. Barea scored five points during an 8-0 run by the Mavericks to boost a four-point lead to 89-77 with eight minutes remaining.

The Heat never got closer than seven the rest of the way, despite the urging from the sold-out crowd at American Airlines Arena.

"All I said was playoff game and play your ass off," said Dallas coach Rick Carlisle. "Dirk Nowitzki is one of the very greatest players in the history of this game and that was validated here tonight.

"He had a tough shooting night in the first half and other guys stepped up and kept us afloat and in the second half. He was amazing."

Dallas Mavericks forward Dirk Nowitzki was named the most valuable player of the NBA Finals after leading his team to their first championship on Sunday.

Nowitzki, who shrugged off injury and illness during the championship series, averaged 27 points and 9.4 rebounds while leading his team to a 4-2 series win over the Miami Heat.