Parker scored 32 points and the San Antonio led by as many as 31 on its way to a 119-96 victory over the Dallas Mavericks, closing out a stressful first-round series Sunday in seven games.
The All-Star point guard was 11 for 19 from the field and 10 for 13 on free throws as Dallas was unable to keep him from attacking the lane, despite a series of hard fouls.
''I just knew that I had to be aggressive if we wanted to have a chance to win the game because of the strategy that the Mavericks chose,'' Parker said. ''They just dared me to score.''
Manu Ginobili scored 20 points, Danny Green added 16 points and Tim Duncan and Kawhi Leonard had 15 points apiece for San Antonio.
Dirk Nowitzki had 22 points and nine rebounds to lead Dallas.
Last season ended for the Spurs with a Game 7 loss in the NBA Finals against the Miami Heat. Facing a much earlier end, San Antonio rode a raucous home crowd and overwhelmed Dallas.
San Antonio advances to face the fifth-seeded Portland Trail Blazers, who upset the Houston Rockets in a six-game series. The series opens Tuesday in San Antonio.
The Spurs got off to a quick start as they had done at home all series, but the Mavericks were unable to respond as they did in winning Game 2 on the road.
Leonard's 16-foot jumper gave San Antonio an 18-7 lead 6 minutes into the game and the lead swelled to 29 with 2 minutes remaining in the first half.
''We gave ourselves a chance but today we got hit by a tidal wave early,'' Dallas coach Rick Carlisle said. ''They had their best game today and we just weren't able to do quite enough to stay in it early.
''It's hard when you get hit with an onslaught early the way the guys did.''
Nowitzki struggled through much of the series, but the Mavericks pushed the Spurs to the brink of elimination behind strong postseason performances from Monta Ellis, Vince Carter, Devin Harris and DeJuan Blair.
''On the court what confounded us was that they've got shooters all the way around,'' San Antonio coach Gregg Popovich said. ''Dirk Nowitzki gets a crowd, if you double him you, you leave a lot of other open shooters. So we played him pretty much one-on-one, so we could stay at home a little bit better. That and the ability to shoot it; spread the floor, run the sets that Rick does and the speed of Harris and Ellis was tough for us to handle.''
Dallas also played a physical series.
There were two technical fouls and two flagrant fouls in Game 7 and two more flagrants reversed upon review.
Parker was assessed a technical with 31.6 second left in the first quarter after making a layup on and jawing with former teammate Blair as the two ran down the court. The two had been talking to each other all series and Parker was clearly frustrated at times with the hard fouls committed by Blair on his drives earlier in the series.
But Parker said it was all in good fun.
''I was just laughing with DeJuan,'' Parker said of the technical. ''That's why it was so funny to get a technical for that, because I was not even cursing at him. DeJuan played four years (for the Spurs). He lived for a year at my house. I love DeJuan.''
Blair was later assessed a flagrant foul for elbowing Ginobili in the face on a drive. After the foul, Blair stared down Popovich, who was screaming at officials over the severity of the foul.
The flagrant foul energized the Spurs, who went on a 14-2 run to take a 51-27 lead with 8 minutes remaining in the first half.
''Everybody was active and kind of focused,'' Duncan said. ''We had very little mistakes.''
San Antonio never led by less than 14 points in the second half.
NOTES: The Spurs were 7-0 in games decided by three points or less during the regular season but were 0-2 against Dallas in such games in their first-round series. . Sunday's game between Dallas and San Antonio was the 50th postseason game this season. It was also the fifth Game 7 of the first round. "'I think it's great for basketball and for the fans,'' Popovich said. "'It drives all the coaches crazy. (But) for the game and everybody, it's been a wonderful thing. "' ... Blair was booed heavily each time he entered the game or committed a foul.