Damon Stoudamire chipped in 17 points and 11 assists and Bonzi Wells had 16 points and eight rebounds for the Blazers, who had lost 10 straight playoff games since Game 6 of the 2000 conference finals against the Los Angeles Lakers.
"We came out and played a full 48 minutes," Wells said. "We just didn't play 24 or 36. We put together a full 48 minutes offensively and defensively, especially defensively."
The Blazers avoided matching the longest postseason losing streak in NBA history, set by the Baltimore Bullets from 1965-70 and tied by the Denver Nuggets from 1988-94.
"We knew we needed this win and we just played hard," said forward Ruben Patterson, who scored Portland's only four points off the bench. "A lot of guys played hard, knowing we didn't want to get swept. Zach played well for us and we just came out in the third quarter with a lot of fire."
Portland had just a 59-58 lead after Dallas' Adrian Griffin made a jumper with 6 1/2 minutes left in the third quarter.
But the Blazers countered with a staggering 21-0 run over the next six minutes. Nick Van Exel, whose buzzer-beating shot from just inside mid-court had given the Mavericks a 52-49 halftime lead, ended the burst with a turnaround jumper with 30 seconds left in the period to make it 82-60.
"I am very disappointed," Van Exel said. "We were right there at halftime and when we came out in that third quarter, I thought we had some pretty good looks at the basket. The shots that we have been making, we just didn't make them tonight."
"Third period, I don't know what to tell you," Dallas Coach Don Nelson added. "I was very disappointed with our performance. We just didn't have any life out there, for whatever reason. We were outplayed and outeverythinged in the third quarter."
The Mavericks shot just four of 19 in the third quarter and committed five turnovers while Portland connected on nine of 19 attempts without a turnover.
"What went right? We made shots and they didn't make shots," Blazers Coach Maurice Cheeks said. "When they're missing shots and we're getting rebounds off those misses, it leads to easy baskets. The big thing, though, is that we came out from the beginning and competed."
"When our jumper is not going, we will always have trouble because we don't have a low-post presence and we are going to struggle," Dallas forward Dirk Nowitzki said.
Portland again was missing injured guards Derek Anderson and Scottie Pippen, but Dallas barely got any production from its starting backcourt. Steve Nash was held scoreless and Michael Finley, who was suffering from flu-like symptoms, made just three of 12 attempts and scored seven points.
Dirk Nowitzki collected 26 points and 11 rebounds to pace Dallas, but had just four points and four boards in the second half. With the game out of hand, he sat out the fourth quarter.
The Mavericks, who scored just 27 points in the second half, shot 37 percent. The Blazers made only 41 percent, but hit 30 free throws to Dallas' 12.
Dallas will try again to wrap up the series at home Wednesday night.
"I thought (Cheeks) got a great performance out of his starters and they played well together," Nelson said. "They got us in foul trouble and got to the free-throw line 42 times. And most of them were deserved."
"I think the players were challenged today," Cheeks said. "The series is not over until someone wins four games. I really don't think Dallas took the game lightly -- no NBA franchise would do that in a playoff situation like this when they could close us out."