"Just play," said Wall of his approach. "I've played through a lot of stuff. I'll be all right."
The third-place Wizards secured their Eastern Conference spot when Detroit and Chicago lost elsewhere, and also moved a game ahead of idle Toronto.
Brandon Jennings had 18 points, one of three Wizards bench players to score in double-figures.
Washington's second unit outscored Brooklyn's 33-14 during a lopsided first half.
That helped coach Scott Brooks give his starters some rest ahead of a five-game road trip that includes visits to Cleveland and Golden State.
"We knew March was going to be pretty demanding," said Brooks, whose team will play eight of its last 10 away from the Verizon Center. "It's a challenge, but our guys are excited about it."
Wall and Beal each played 24 minutes, with Wall playing his second-fewest in a game this season.
That was a welcome break for the four-time All-Star point guard, whose symptoms had convinced him to skip the morning shootaround.
"I've still got a headache, (but) it's not as bad as it was this morning," Wall said. "I took some medicine. I slept just about all day until like 4:30. So still taking medicine, still trying to do as much treatment as I can and prepare myself for tomorrow."
Justin Hamilton scored 20 points off the bench to lead the Nets a day after Brooklyn beat Phoenix 126-98 for its second-largest win of the season.
The Nets actually led by nine early, then trailed by as many as 28 after Washington outscored Brooklyn 55-18 during a 15-minute stretch that went deep into the second quarter.
"Things don't go your way all the time, and I feel like we could've handled it a little differently," said Rondae Hollis-Jefferson, who added 19 points for Brooklyn. "But that's on us."
Nets: Suffered their 30th road loss off the season. ... Allowed their most points since a 130-116 loss at Portland on March 4.
Wizards: Swept the season series with Brooklyn for a third time in four seasons ... Improved to 18-11 in games that are part of back-to-back sets. . Wall and Jennings each finished with nine assists.
Before the game, Brooks explained why he didn't automatically sit Wall, who has played in 70 of Washington's 72 games.
"Our medical team and our players, that's their expertise," Brooks said. "I like guys that want to play. He's not going to put himself in harm's way. ... But if he feels like he can play, I think that's a great asset and a great trait to have as a player and as one of the leaders of the team."
"THE PERFECT ROLE"
Bojan Bogdanovic scored 17 points in his first game against Brooklyn since leaving the Nets for Washington at the February trade deadline. He's averaging 14.8 points in 17 games off the bench.
"I think he's in the perfect role for him right now," Nets coach Kenny Atkinson said. "It's like being a receiver playing with a great quarterback. He kind of sits there in the corner and Wall throws those 1,000 mile-an-hour fastballs to him."
After playing at home on Thursday, the Nets took the unusual step of traveling to Washington on the day of their game.
"Obviously, the result isn't very good. So, if we're just going on the result, it wasn't a smart move by the coach," Atkinson said. "But I don't regret it. It's part of trying to find out how to be more efficient in what we do."
Nets: Close a two-game road trip at Atlanta on Sunday.
Wizards: Begin their road trip at Cleveland on Saturday.
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