Leonard provided 17 points with six rebounds while Duncan added 15 and eight as the Spurs took a fourth straight win and fifth in six games.
San Antonio held Timberwolves star Kevin Love to 14 points and seven rebounds.
Nikola Pekovic led Minnesota with 22 points and six boards.
Rosie O'Donnell unveils nearly 50-pound weight loss
Members of Congress to keep receiving porn magazine