The Cavs nailed 18 shots from beyond the arc en route to a 125-103 rout of the Toronto Raptors in their East playoff series.
Leonard also delivered eight assists and seven rebounds for the Spurs, who now travel to Houston for games three and four of the best-of-seven second round Western Conference series.
"We were focused," Leonard said. "We lost by 30 points last game so we didn't want to disappoint the fans."
San Antonio's win could prove to be costly because of an injury to guard Tony Parker. The Frenchman had to be carried off the floor by teammates with 8:43 remaining after suffering a left leg injury.
Meanwhile, LeBron James reached another milestone and the Cleveland Cavaliers nailed 18 shots from beyond the arc en route to a 125-103 rout of the Toronto Raptors in their East playoff series.
San Antonio led 97-83 at the time of Parker's injury. The incident took place when Parker missed a short layup and landed underneath the Rockets' basket. He had scored 18 points before leaving the game.
Parker clutched his left knee as he lay on the floor. He was carted off by teammates Dewayne Dedmon and Dejounte Murray and did not look up as the crowd chanted his name.
"I just hope he is OK because we need him the next game," Leonard said.
Parker is expected to undergo an MRI scan on Thursday.
Spurs coach Gregg Popovich said of Parker, "It is not good."
LaMarcus Aldridge scored 15 points for the Spurs while Jonathon Simmons added 14 points and Danny Green scored his 12 points all in the first half.
In Cleveland, James became the NBA's second all-time leading scorer in the postseason with a 39 point performance as the Cavaliers crushed the Toronto Raptors in game two.
James nailed a three pointer in the second half to surpass Kareem Abdul-Jabbar (5,762 points) for second place. Michael Jordan is first with 5,987 playoff points.
"You find somebody to stop LeBron in these moments, I'll give you $100," Toronto's DeMar DeRozan said.
The win gives Cleveland a 2-0 series lead but game three is in Toronto on Friday.
James also joined Ray Allen, Reggie Miller and Manu Ginobili to become the fourth player in league history to make 300 playoff three-pointers in a career. And he now has 89 playoff games with at least 30 points, which moved him past Kobe Bryant. Only Jordan (109) has more.
James scored 17 points in the third quarter to give Cleveland a 99-73 lead heading into the fourth.
"I'm feeling pretty good," James said. "My teammates do a great job of putting me in position. My coaching staff do a great job of putting me in position to be successful.
"And, I put a lot of work in on my craft and I live with the results. Just blessed I'm able to make a few plays tonight to help us win another game."
Kyrie Irving added 22 points and 11 assists for Cleveland, who also received 18 points from Channing Frye. Iman Shumpert came off the bench to score 14 for the Cavaliers, who easily won game one 116-105 on Monday.
The Raptors were led by Jonas Valanciunas who had 23 points. All-Star guard Kyle Lowry scored 20 points but injured his left ankle in the third quarter and was out of the game for good by the fourth.
The Raptors have never won a playoff series when trailing 0-2 and are now a dismal 1-6 in game two's on the road.
DeRozan, the Raptors' leading scorer this season, was limited to five points on two-of-11 shooting.
"It sucks. To lose like we did," DeRozan said. "Now I just have the added time having to wait till Friday night to redeem myself."