The sixth-seeded Mavericks rode Dirk Nowitzki's 31-point performance to a 106-93 Game Five victory in San Antonio to claim their best-of-seven Western Conference series by a 4-1 margin.
Nowitzki hit 11-of-17 shots for game scoring honours but the German forward received plenty of support as the Mavericks turned back San Antonio's two-man tandem of Tim Duncan and Tony Parker.
Duncan finished with 30 points and Parker added 26 points and 12 rebounds, but the remainder of the team had just 37 points.
Dallas backed up Nowitzki with five other players in double figures as the Mavs advanced to the second round for the first time in three years. They will play the winner of the Denver-New Orleans series in the conference semifinals.
"We're not finished yet," Dallas's Jason Terry told reporters after completing a 19-point effort.
Birthday boy Josh Howard added 17 and center Erick Dampier contributed 11 points and 12 rebounds.
"This is our best basketball of the year," Dampier said. "That's a big key for us, to be playing well at the right time." San Antonio, who were without Manu Ginobili, failed to make it past the first round for the first time since 2000.
"They're a better team than we are right now," Spurs coach Gregg Popovich said. "We made runs, but every time we got back into the game, they made more big shots. That's why they won the series."
Houston, who could have joined the Mavericks in the second round with a win, lost 88-77 at Portland but still lead the series 3-2.
In Portland, the Trail Blazers went on a 15-0 fourth-quarter run to stop the Rockets. Brandon Roy and LaMarcus Aldridge both scored 25 points for Portland. Luis Scola led the Rockets with 21 points, while Yao Ming added 15 points and 12 rebounds.
The series moves back to Houston for Game Six tonight.