Washington won the series four games to two and advances to the second round to meet Boston, which eliminated Chicago in six games.
"John is a heck of a player," Brooks said. "He's carried us with his leadership. We have a lot of good players, with his leadership and with Brad's leadership has been great. For young players in this league, I couldn't ask for two better guys to lead our team."
Wall scored 20 points in the first half and finished with 42 points -- a career playoff best -- on 16-of-25 shooting. Beal had 17 in the first half and finished with 31 points on 11-of-17 shooting.
Wall also had eight assists, four steals and two blocked shots. His 16 field goals set a career best for playoffs.
The duo finished the series with 332 of the team's 640 total points in six games, 51.8 percent of Washington's offense.
"Wall and Beal were special," Atlanta coach Mike Budenholzer said. "Credit to them."
Atlanta guard Kent Bazemore said, "John Wall was huge tonight. We couldn't seem to contain him. And Bradley Beal had a solid game, too."
Atlanta was led by Paul Millsap, who finished with 31 points, nine rebounds and seven assists in 46 minutes. Dennis Schroder had 26 points and 10 assists, his second straight double-double. Tim Hardaway Jr. scored 13 points, but was 5 of 18 from the floor. Dwight Howard had nine points and seven rebounds, but did not play in the fourth quarter.
The Wizards led by 22 points in the second half, but Atlanta twice trimmed the lead to three points. Washington answered with six consecutive points, the last basket being a jumper by Wall with 3:31 left that restored the nine-point lead.
"It's really not fair for a point guard to do what he does," Brooks said. "There's only one other player (LeBron Jones) in the league who can do what he does and we all know who that is. John does it every game. That's the sign of a champion."
Budenholzer said, "I felt like we had an opportunity to dig out of another big hole, but a couple of plays down the stretch changed the game and they were able to make a couple of plays."
Washington got off to a hot start, with Morris making a pair of 3-pointers in the first four minutes to help stake the Wizards to a 17-10 lead. They led by as many as 10 points when Kelly Oubre Jr. made a 3-pointer, one of four by the team in the first quarter, and wound up with a 30-23 lead.
The first quarter turned physical early. Howard knocked Washington's Jason Smith to the floor with an elbow to the chin. Officials reviewed the play, but ruled it a common foul rather than a flagrant foul.
Another incident nearly caused a fight with 51.9 seconds left. Beal scored on a breakaway slam and tumbled into the first row, believing incorrectly that he had been pushed by Atlanta's Kent Bazemore. Words were exchanged and both teams clustered near the basket. Bazemore and Smith were assessed technicals for pushing each other. There were no further incidents between the two teams.
Washington continued to take advantage of Atlanta mistakes and led 65-46 at halftime. The Hawks had 15 turnovers in the first half, leading to 20 points for the Wizards.
"We obviously did not play well in the first half," Budenholzer said. "We dug ourselves a big hole."
The Wizards shot the ball exceptionally well in the half. The Wizards made 65.8 percent of their shots, including 6 of 10 on 3s, which offset the above-average 50 percent field-goal shooting by Atlanta.
Washington led by as many as 22 points in the third quarter, but Atlanta refused to go away. Schroder scored 14 points in the quarter and the Hawks cut the margin to seven when Howard followed a missed shot with a slam. Washington took an 89-82 lead into the fourth quarter.
"Defensively, we were able to piece together some consecutive stops, get some turnovers, get out in transition, attack the basket," Budenholzer said. "When you're going to make a run, you've got to put stops back to back to back and that fueled our offense."
NOTES: Washington C Jason Smith entered the game with 7:33 left in the first quarter. It was uncertain whether he would play because of sprained left knee. ... The Wizards improved to 8-0 all-time in a series where they had a 3-2 lead. ... Inactive for Washington were C Ian Mahinmi (left calf) and F Chris McCullough. Inactive for Atlanta for were F Ryan Kelly and F DeAndre Bembry.