Leonard also had seven assists, three rebounds and three steals in the 128-105 win on Wednesday at Staples Center in Los Angeles. Fellow Clippers All-Star Paul George chipped in 23 points, 10 rebounds and seven assists.
"We tried to come out and bring energy and intensity and share the ball." Leonard told reporters.
Leonard wore a clear plastic mask throughout the game to protect his mouth, after he had eight stitches put in the area after he took an elbow to the face from teammate Serge Ibaka.
Portland shot just 31.6% from 3-point range and 42.1% from the floor. Los Angeles made 47.4% of its 3-point attempts and 49.5% of its field goals.
The Clippers used a balanced offensive attack to earn a 37-26 lead through the first quarter and 76-57 edge at halftime. Leonard then erupted for 16 points in the third quarter to push the Clippers lead to 107-85 at the start of the final frame.
The Clippers outscored the Blazers 21-10 over the final 12 minutes to secure the win.
Blazers stars C.J. McCollum and Damien Lillard scored 25 and 20 points, respectively, in the loss. Enes Kanter had 10 points and 10 rebounds off the Blazers bench.
"They were active and they showed their length," Lillard said of the Clippers. "They played with energy and played physical. They caused [turnovers] and some of that with us. Our communications wasn't good and we missed open shots."
"Whatever sets we are running, we just want to make sure we make the right play," Clippers coach Tyronn Lue said. "With our team, as constructed, everybody on our team can make a play. That makes us dangerous."
The Clippers (4-1) face the Utah Jazz at 9 p.m. EST on Friday at Vivint Arena in Salt Lake City. The Blazers (2-2) battle the Golden State Warriors at 10:30 p.m. EST on Friday at Chase Center in San Francisco.