Parker scored six of San Antonio's final nine points, hitting a pair of jumpers and a layup after missing his first two attempts of the quarter.
"They did what they do best, and that's going to Duncan and Parker," Lee said. "And have their role players do what they do."
Golden State led for all but 34 seconds in the first half.
The teams combined to start the game 2 for 12 from the field. The Spurs' first basket came 3 minutes in on Duncan's 19-foot jumper.
Golden State closed the first quarter on a 13-4 run but Gary Neal threw in a 3 at the buzzer to pull the Spurs to 26-19. Carl Landry had six points during the run.
Landry continued his dominance in the second quarter, going 7 for 10 while scoring 15 points. He did not score in the second half.
The Spurs had an opportunity to take the first-half lead, but Green missed a hurried 3-pointer after Splitter almost dribbled the final 3 seconds off. Popovich stormed onto the court, yelling at Splitter and Parker.
The start of the second half was delayed 15 minutes while one rim was fixed because the top screws were loose.
The Spurs tied the game at 58 midway through the third quarter when Stephen Jackson, Parker and Duncan quickly rotated the ball across the court to find an open Green for a 3. Duncan hit a pair of free throws on the following possession to give the Spurs a 60-58, their first since early in the first quarter.
The Spurs went on an 18-11 run after Duncan's free throws to take their largest lead at 78-69 with 27.3 seconds left in the third.
NOTES: Warriors C Andrew Bogut (ankle), G Stephen Curry (ankle) and G-F Brandon Rush all missed the game with injuries. ... Spurs G Manu Ginobili missed his second straight game and sixth of the season. ... Former Spurs G Pete Myers is an assistant coach with the Warriors. He averaged 4.7 points while playing 22 games for the Spurs in 1987-88 and eight in 1990-91. ... Parker has led the Spurs in scoring in 22 games, and 33 times in assists this season. ... The Spurs have swept the last four season series with the Warriors. ... Lee is the only player averaging 19 points, 10 rebounds and three assists per game this season. ... Thompson is the son of two-time NBA champion Mychal Thompson, who was traded by the Spurs to the Los Angeles Lakers midway through the 1987 season.