Mystics guard Natasha Cloud goes up for the layup around Los Angeles Sparks forward Candace Parker during Thursday’s 96-64 Washington win.. (Katherine Frey/The Washington Post)

During a timeout in the fourth quarter of the Washington Mystics’ 96-64 victory in Thursday night’s WNBA quarterfinals, guard Natasha Cloud stood alone near half court, shimmied her shoulders and offered a few quick dance steps.

Players on the visiting Los Angeles Sparks, meanwhile, had hands on their hips and breathed heavily while they waited for teammate Nneka Ogwumike to attempt two foul shots with the outcome long since determined.

She missed both, providing further indication of fatigue throughout the Los Angeles roster that fueled the Mystics’ fast-break frenzy as they advanced to the WNBA semifinals for a second straight year. No. 3 seed Washington next hits the road to face the No. 2 seed Atlanta Dream on Sunday in Game 1 of the best-of-five series.

“Extremely gassed,” Cloud (13 points, seven assists) said of the sixth-seeded Sparks, who logged thousands of miles in travel over the later portion of their schedule. “So we knew that, and we took that to our advantage. We’re a well-conditioned team, so we can go four quarters of that type of pace.”

Every Mystics starter scored in double figures, led by Elena Delle Donne’s game-high 19 points. The first-team all-WNBA selection added a game-high 12 rebounds in addition to four assists at Smith Center, which is serving as Washington’s home court during the playoffs because of renovations at Capital One Arena this month lasting into September.

Washington had a franchise-high 28 assists, led by guard Kristi Toliver’s game-high nine (to just one turnover), shot 57 percent and made all 13 of its free throws. The Mystics committed just nine turnovers and finished plus-seven in rebounding.

“We preach all the time, there are three things we need to win playoff games, and that’s turnovers, free throw difference and rebounding, and we won all those tonight, besides shooting the ball well,” Mystics Coach Mike Thibault said. “We did just about everything you hope as a coach. As a coach, you worry about what are we going to do about late-game plays.

“We didn’t have to worry about that tonight.”

The Mystics also got an offensive boost from a defensive specialist. Center LaToya Sanders finished with 14 points on 7-for-11 shooting with seven rebounds and four assists, but her two early blocks set the tone for Washington’s defensive gem.

Sanders played a significant role in helping to limit Sparks all-star Ogwumike to eight points on 2-for-10 shooting. The 2016 WNBA MVP has been dealing with an illness and had two points with more than eight minutes left in the fourth quarter before amassing the rest of her scoring at the free throw line.

Los Angeles shot 34 percent and went 6 for 22 (27 percent) from three-point range. The starting backcourt of Chelsea Gray and Riquna Williams combined to shoot 2 for 12 from beyond the arc, a stark contrast to their 7-for-14 three-point shooting in a 75-68 first-round win against the Minnesota Lynx on Tuesday at Staples Center.

The Sparks, the 2016 WNBA champions and last year’s WNBA Finals runner-up, arrived in the District on short rest, having boarded a commercial flight across the country Wednesday and not set foot in Smith Center until a shoot-around Thursday morning.

“Our mentality is that we play the hand that we’re dealt, so we don’t have any excuses,” Sparks Coach Brian Agler said. “My hat’s off to Washington. They played really well, made the right plays offensively, found open people, hit shots, made it difficult for us at our offensive end. They were the better team today, no question about that.”

The quick turnaround for the Sparks left little time for recovery for all-star forward-center Candace Parker, limited to two points in nearly 30 minutes with an illness in the Sparks’ playoff opener.

The two-time WNBA MVP, most recently in 2013, was back in fine form for the second round, staking Los Angeles to an early lead with an acrobatic layup followed by a three-point play.

But the Mystics countered with Delle Donne, who scored or assisted on 10 of 13 points during a surge late in the first quarter that produced Washington’s first double-digit lead. The margin swelled to 50-29 by halftime, with the last eight points scored by reserve forward Tianna Hawkins.

The first half also concluded with physical play in which Hawkins (10 points) and Williams were assessed double technical fouls while jostling for a loose ball underneath the Mystics’ basket.

“It was just trusting in the next pass and trusting in one another,” Delle Donne said. “Not having to force any situation and just knowing if we continue to move the ball, they were going to break down at some point. We’ve built a great culture here. Our trust with one another has grown this entire season, on defense and on offense. Tonight it kind of all just came together.”