This first-round series, which would have been fitting as a Western Conference finals, was the most anticipated. So far at least, it has more than delivered.
Duncan finished with 40 points and 15 rebounds.
Michael Finley sent the Spurs to overtime with a last-second 3 from the wing, tying the game at 93.
The Suns had controlled play for the first three quarters, leading by as many as 16 points despite early foul trouble for Shaquille O'Neal. The Suns had a six-point lead with a quarter left in regulation.
The Spurs took their first lead of the game late in the fourth quarter, but were down 93-90 with 1:10 to go after Leandro Barbosa's fast-break layup.
With 15 seconds on the clock, Finley tied it at 93 for the Spurs.
Two-time MVP Duncan stole the show in the first overtime. With his team down 104-101, Duncan found himself all alone at the 3-point line. After only a slight hesitation, he fired the ball and made it with 3 seconds to play. It was Duncan's first 3 of the season. He was 0-of-4 previously.
In the second overtime, Shaq's dunk tied it at 112 with 1:33 to play. Ginobili's layup made it 114-112 San Antonio.
Steve Nash missed a key 3 from the corner with less than a minute to play. After a long and risky inbounds pass that crossed the width of the court to the Spurs' Brent Barry, the Suns fouled, and Barry sank one of two from the line to make it 115-112 Spurs.
With 15 seconds on the clock, Nash fired another 3, sinking it this time to tie the game at 115.
Then Ginobili drove the lane and his layup fell with 1.8 seconds left for the win.
Tony Parker added 26 points for the Spurs, and Ginobili had 24.
Amare Stoudemire, who fouled out with 12 seconds left in the first overtime, led the Suns with 33 points. Nash had 25 points and 13 assists, O'Neal scored 11 points.
The Suns and Spurs met last season in the second round in what many dubbed the real finals. San Antonio won in six tense and testy games on their way to a fourth NBA title.
This year's rematch comes in the first round in the hyper-competitive Western Conference.
Phoenix acquired O'Neal in a blockbuster midseason trade for a series such as this one to give the run-and-gun Suns a defensive boost.
Notes: There were quite a few orange T-shirts dotting the crowd. ... The Spurs have eliminated the Suns in three of their last four postseason appearances. ... Raja Bell scored 14 points for the Suns. Barbosa and Boris Diaw each added 12. ... Finley had 13 points for San Antonio, and Kurt Thomas, who played for the Suns last season, grabbed 10 rebounds.