Gooden's 3-pointer broke a 94-94 tie with 2:37 left. Trevor Ariza then scored off an offensive rebound with 44 seconds left and Wall capped it with dunk.
The Nets, who went the final 6:22 without a field goal, were led by Marcus Thornton's 19 points. Joe Johnson added 16 and Paul Pierce had 15.
Washington completed a sweep of the season series (3-0) and moved ahead of Brooklyn for fifth place in the Eastern Conference.
Trailing 82-72 early in the fourth, the Wizards went on a 15-4 run keyed by Gooden (8 of 11 from the field) and Al Harrington.
Harrington started things off when he scored four points and picked up a steal that led to a basket by Bradley Beal.
Then with the Wizards trailing by three, Gooden hit a layup and then a jumper from the wing that gave Washington an 87-86 lead, its first of the half.
Thornton answered for New Jersey, making a 3 and following with a driving bank shot to put Brooklyn up 91-87 midway through the quarter.
The Wizards tied it at 92 on Wall's free throw.
Wall nearly brought the Wizards all the way back in the third, when he scored 15 points. The Wizards cut a 12-point deficit to 63-62 before Brooklyn went on an 8-0 run and led by seven after three.
With the score tied midway through the first quarter, Deron Williams hit a layup and a 3 to spark the Nets and Brooklyn led 26-19 after one.
The Wizards pulled to within 33-32 on Martell Webster's 3-pointer early in the second quarter.
Former Wizard Andray Blatche (eight points in the second quarter) scored inside and Thornton hit his second 3 of the quarter to push the lead back to seven.
The Nets shot 55 percent (22 of 40) in the half.
NOTES: The Wizards improved to 17-16 at home. ... Washington last swept the Nets in 2009-10, when they took all four meetings. . Brooklyn F Andrei Kirilenko returned after missing two games with a sprained ankle. . Nets C Jason Collins, who signed a contract for the remainder of the season Saturday, didn't see action. . Pierce (24,819) passed Patrick Ewing for 18th place on the NBA's career points list.