SAITAMA, Japan — There were 13 seconds left on the clock when Kevin Durant found himself gliding to the basket with no one around him.

He ascended smoothly to the rim and dunked the ball with two hands. When the buzzer sounded moments later, Draymond Green jogged over to Durant, grabbed his hand and thumped his chest. It seemed like a gesture of both celebration and appreciation.

Having one of the most complete scorers in the universe on your basketball team has its advantages.

That is a lesson Green and his United States teammates were happy to learn on Tuesday afternoon — a luxury they have needed to exploit over these past couple weeks — as Durant took control of their do-or-die Olympic quarterfinal matchup against Spain, scoring 29 points to lead the Americans to an initially nervy, but ultimately comfortable, 95-81 win.

“Kevin Durant was great,” Green said. “He was who we need him to be. He showed why he’s arguably the greatest player in the world.”

The win sent the United States to the semifinals of the men’s tournament, where they will meet the winner of a contest between Argentina and Australia.

Since the start of their preparations for the Games, the American players have spoken openly about the fact that they are still learning to play together as a group, rather than merely an assemblage of individual stars. They lost two exhibition games before leaving home and then started their Olympic campaign with a defeat against France.

The good thing, Green said, is that they continue to improve. The only bad thing, he said, is that there is not much time remaining for them to figure it out.

“I think the potential of this team is endless,” Green said. “Unfortunately we’ve got two games left, so we need to make sure we’re continuing to get better each and every time we step on the floor. I think that’s what we’ve done.”

However much they improve, however many question marks remain, they have the ultimate insurance plan in Durant, who proved again on Tuesday that he can undo the shackles of even the most rigorously drilled defenses in the world.

The United States got off to a slow start, settling for outside shots, and failing to make them, as Spain built a 10-point lead late in the second quarter. The Americans shot only 38 percent from the field in the first half, making only 4 of 17 attempts from 3-point range.

But Durant and his teammates got more aggressive before the halftime break. They worked the ball inside, unsettling the Spanish defense, and finished the quarter on a 14-4 run. That sent the teams to the locker rooms tied at 43-43.

“If we drive it to the paint, there’s going to be two or three guys converging, then we can get the 3,” Durant said. “If we come out just chucking 3s up early, if we’re not hitting them, it’s going to look bad.”

As Durant got hot from 3-point range in the third, the Americans took control of the game and never let go. Durant finished the game 10 for 17 from the field, including 4 for 7 from 3-point range.

Afterward, Durant said he was still just getting comfortable with his role. His remaining opponents may be watching warily to see how comfortable he gets.

“In this setting, it’s always hard to get your footing as an individual player because you don’t want to step on toes, you’re coming in and out of the game, you’re not playing as many minutes, getting as many shots,” Durant said. “But I love how we’ve stuck with it through this whole period of time, and guys are starting to figure out what to do.”

The Spanish, bigger and better drilled, used their size as an advantage whenever they could. They won the rebounding battle, 42-32, and cashed in on several second-chance opportunities around the basket.

Ricky Rubio was their main instigator on offense, leading all scorers with 38 points.

Asked about the importance of Durant, U.S. Coach Gregg Popovich drew a comparison to Rubio’s role in the Spanish team.

“They’re both great players, and they’re both hard to stop,” Popovich said, before adding about Durant: “In these games, every team has people like that, that they depend on to come through, and he certainly did.”

A gold medal run would put an exclamation mark on a long season for Durant, who missed the entire 2019-2020 N.B.A. season after tearing his right Achilles’ tendon. He returned to the Nets this season and averaged 34.2 points during their 12-game postseason run.

“Kevin is a rhythm player, and figuring out the rhythm and flow is important,” Green said. “We’ve got that figured out now, and we allowed him to do what he’s great at, and he was great.”

The absence from the United States team (and the Olympic tournament) of some of the game’s biggest stars — LeBron James, Stephen Curry, James Harden — has sharpened the spotlight on Durant. But he seems to be taking it in stride, asserting his identity in increasingly significant ways, even as he seemed to take little pleasure on Tuesday in advancing to the semifinals.

“We’re supposed to be here,” Durant said. “For us it’s about getting a gold.”