Burton scored Nevada's final nine points, including two 3-pointers to help hold off the Huskies, which had rallied from an 18-point second-half deficit to take a 61-60 lead. But Burton answered with a three-point play of his own and the Wolf Pack never trailed again.
Malik Story had 15 points and eight rebounds for Nevada (5-4). Devonte Elliott scored nine of his 11 points in the second half.
C.J. Wilcox scored 15 of his 21 points in the second half to lead Washington (4-4), which had won two straight. Scott Suggs added 19 points, Abdul Gaddy had 16 and Aziz N'Diaye had 11.
Nevada led 53-35 with 14:35 remaining before the Huskies used a 20-2 run to tie the game at 55 with 7:34 remaining.
Burton nailed a 3 from way out top to make it 70-66 and added a second 3-pointer while falling back near the Nevada bench to give the Wolf Pack a 73-68 lead with 1:58 left. He added three free throws to seal the win.
"A good team came out and beat us with two super-human 3-point shots by Deonte Burton," Washington coach Lorenzo Romar said. "They were highly contested, well-defended shots, he's just a heck of a player and hit two big shots."
Burton, who scored a career-high 31 last season against Washington, said he had confidence both shots would drop from beyond the arc. He made 3 of 5 on 3-pointers in the game.
"On one, my teammate was in trouble and the shot clock was winding down and I had to pull through," Burton said. "On the other one, my number was called and I had to come through for my teammates and just shoot it like I shoot it in practice."
Wilcox played Burton tight on both shots.
"The first one was a tough shot and the second one I actually tipped," Wilcox said. "I thought it was going to be an air ball but once he got going, he could make shots like that."
Burton and Story have combined for nearly half of Nevada's points this season. The backcourt pair combined for 44 against the Huskies.
"He's been my backcourt mate for three years so I've seen it all the time," Story said about Burton's performance. "I know what's he's capable of doing. That's what he does, that's what he's known for and he's going to continue it the rest of the year."
Nevada coach David Carter watched his team snap a two-game losing streak.
"(This game) helps us a lot," Carter said. "Washington's a great team and they are going to win a lot of games in the Pac-12. Any time you can win on the road it boosts your confidence."
Suggs, who missed the previous three games with a sprained foot, hit a 3-pointer to give Washington its first lead of the game at 61-60 with 5:17 left.
"Great teams are going to battle back," Burton said. "We had to throw the first punch but we kind of relaxed when we had the lead and they took advantage of it."
Gaddy had a steal and a dunk to tie the game at 55 with 7:34 left and complete a 20-2 run. Gaddy's steal came right after a put-back by N'Diaye.
"We dug ourselves a hole with too many defensive lapses in the first half," Romar said. "In the second half, we had a courageous effort in the comeback. We guarded a lot better but we missed some easy ones late in the game."
Story scored eight and Burton seven during a 19-9 run to help give the Wolf Pack a 53-35 lead with 14:34 left.
But the Huskies scored 12 straight to cut the lead to six with 11:01 remaining before Burton hit a jumper to stop the streak.
Gaddy had four points and played just 10 minutes in the first half as he went to the bench with three fouls with 10:57 remaining.
Washington starting guard Andrew Andrews missed the game with a sprained ankle suffered Thursday in practice. He is out indefinitely.