Jamison had 33 points and nine rebounds and Butler scored 30 for the Wizards, who held off the Sacramento Kings for a 110-107 win on Wednesday night.
Andray Blatche added 20 points for Washington. The Wizards had lost seven of their eight previous games and are 3-17 on the road.
The Wizards, who have struggled with injuries and have nine wins on the season, are hoping for a fresh start for the second half of the season.
"This is our team, there is no help coming," Butler said. "We have a lot of young guys playing right now and I'm getting more and more of a feeling of what they like to do out there."
The Wizards entered the game as one of the NBA's lowest-scoring teams while the Kings are second in points allowed.
"It's been a grind, losing is not fun. People talk bad about you and you know you're better than the way you are performing and producing," said John Salmons, who had 24 points for the Kings, who have one more win than Washington.
After hearing boos in the third quarter and entering the fourth down by 19 points, the Kings showed some life.
Point guard Beno Udrih led the way, finding holes in the defense on drives to the basket and hitting outside shots. Udrih's 3-pointer with 43 seconds left cut the lead to 104-102.
A 3-pointer by Francisco Garcia reduced the Wizards' lead to 108-107 with 3.9 seconds remaining.
The Kings immediately fouled Blatche, who responded with two free throws and put the Wizards ahead by three points with 3.4 seconds left. Garcia missed a corner 3-pointer with a second left that could have sent the game into overtime.
"They got it going and started making 3-point shots, which gave them lots of momentum," Washington coach Ed Tascott said. "We were barely able to hold them off. Wins on the road don't have to be elegant, they don't have to be stylish, they just have to be wins."
Udrih had 16 of his 24 points in the fourth quarter when the Kings outscored the Wizards 37-21. Sacramento made 12 of 25 3-pointers, hitting six to fuel its fourth-quarter comeback.
Kevin Martin added 22 points and Garcia had 14 for the Kings, who have dropped three straight and four of five.
"Our mindset is that we come into the arena and we get the win," Udrih said. "We can't think like that, we are not in that position. We've got to come out and play hard."
Having failed to score 100 or more points in 11 of the past 12 games, the Wizards went over the 100-point mark on a Darius Songaila basket with 5:04 left in the game.
After a strong first half, Butler was difficult to stop in the third quarter. He and Jamison both scored 13 points as the lead reached a high of 21 points and Washington took an 89-70 lead into the fourth period.
The Kings have lost seven straight to the Wizards over the past four years and are 0-16 against the Eastern Conference this season.
"We knew they hadn't beaten an Eastern Conference team and we didn't want to let it be us," Butler said.
Averaging 29 points in the previous nine games, Martin had a poor first half, missing 5-of-6 shots, scoring four points. Martin got untracked in the third quarter when he made four 3-pointers and scored 16 points, yet the Kings were still outscored 35-26.
Butler scored 15 points and both Jamison and Blatche had 12, helping the Wizards maintain control throughout much of the first half. Salmons scored 10 points for the Kings, who trailed 54-44 at intermission.
JaVale McGee's mother, Pamela McGee, played for the Sacramento Monarchs in the inaugural season of the WNBA. ... Although they shot 52 percent overall, the Wizards were 2-of-14 on 3-pointers.