Manu Ginobili scored 26 points and San Antonio survived blowing a 22-point lead.
The Spurs got payback after the Mavericks eliminated them a year ago, and will play the Phoenix Suns in the Western Conference semifinals. San Antonio beat the Suns in the playoffs in 2007 and 2008. The opening game is in Phoenix on Monday.
Dirk Nowitzki nearly carried Dallas to a comeback; getting 25 of his 33 points in a remarkable second half. But the Mavs still stumbled to their third first-round exit in the past four years.
George Hill had 21 points for the Spurs, who are coming off their worst regular season in the Tim Duncan era - making this series all the more impressive.
It will technically go down as an upset. San Antonio is only the fifth No. 7 seed to win a first-round series, and the first since the opening round became a best-of-7 in 2003. It hadn't been done since New York beat Miami in 1998.
But with a healthy Big Three and a championship pedigree, the Spurs could hardly be called underdogs. And with no clear favorite in the West, they might be as good a final pick as any.
As for Dallas, it was yet another early playoff disappointment.
It comes three years after the Mavericks came into the postseason as the No. 1 seed, only to be knocked out by No. 8 Golden State. The Mavs were the NBA's best road team in the regular season, but went 0-3 in San Antonio and couldn't pull themselves out of a 3-1 deficit.
This one was especially tough for team owner Mark Cuban, who plunked down an extra $30 million for a deal at the trade deadline that brought Caron Butler from Washington.
Butler scored 25 points and rookie Rodrigue Beaubois had 16 points. But aside from them and Nowitzki, no other Dallas player scored more than six points.
In Portland, Jason Richardson scored 28 points, including five 3-pointers, as Phoenix also advanced with a 4-2 series win over Portland.
The Suns went up 53-41 at halftime and led by as many as 16 points in the second half before Portland fought back to tie it 76-76.
Amare Stoudemire's layup and Goran Dragic's rebound put the Suns in front 80-76, and Phoenix extended it on two consecutive lay-ups and a 3-pointer from Richardson to suddenly make it 87-78 with 4:36 left and the game was safe.
Stoudemire finished with 22 points for the Suns.
Martell Webster had 19 points for Portland, which failed to advance out of the first round for the second straight year. Brandon Roy had 14 points for the Blazers in his first start of the series after minor knee surgery.
Grant Hill of the Suns advanced past the first round for the first time in his career. Phoenix is 6-1 in their past six potential series-clinching games.
Portland has never won a series that they have trailed 3-2.
