Leonard hit 11 of 15 shots after not scoring at all in the first quarter and Patty Mills scored 15 points off the bench for the Spurs (18-4), who played without Tony Parker after he bruised his left knee against Milwaukee on Wednesday night. San Antonio overcame a slow start to shoot 52.7 percent.
The Spurs moved past the 1969-70 New York Knicks to take sole possession of the second-best road start to begin a season in NBA history. The Golden State Warriors started 14-0 last year.
Zach LaVine scored 25 points for the Timberwolves. Karl-Anthony Towns had 11 points and 14 rebounds, but shot just 3 of 16.