PHOENIX -- Asked where his buzzer-beating basket from three quarters of the way down the court ranks among the longest of his career, Grant Hill shrugged, "Top 20."
Hill banked it in from the Los Angeles 3-point line to give Phoenix a 67-55 halftime lead, and the Suns went on to beat the Clippers for the sixth straight time.
Dudley, scoreless in the Suns' home loss to Oklahoma City on Wednesday night, made 4 of 5 3-point attempts.
"Usually when you have it going, your teammates find you," Dudley said. "That's all it was."
The Suns shot 54 percent, including 12 of 24 from 3-point range. They entered the game on a two-game losing streak, both losses coming at US Airways Center, after starting the season 10-0 at home.
"We just needed to have a good win to try to restore a little bit of our confidence," Phoenix coach Alvin Gentry said.
Los Angeles was without Marcus Camby after the first quarter because of a sore left knee.
The Clippers shot just 40 percent, and no one struggled more than Eric Gordon, who scored 11 points on 4 of 15 shooting.
"Grant Hill gave them that cushion to start the second half," Clippers coach Mike Dunleavy said, "then we made some mistakes and some turnovers and they make you pay the price."
Leandro Barbosa scored 12 points in his return to the Suns after missing 12 games because of a sprained left ankle.
The Suns got off to a listless start, with the Clippers grabbing 14 of the game's first 15 rebounds and taking a 16-8 lead.
Gentry called time out to remind his players this is exactly how they had played on Wednesday night. At the time, the Clippers had outrebounded Phoenix 14-1, a trait that had figured largely in the loss to Oklahoma City.
"I don't know if we don't realize we're not the greatest rebounding team in the world but we just give up offensive rebound after offensive rebound after offensive rebound," the Suns' Steve Nash said. "Then they start crashing the boards and going to the hoop hard, so we had to really make a stand to stop them from continuing to drive it down our throats and going for the rebound."
Nash's driving layup kicked off a 12-2 run that put Phoenix up 20-18 on Richardson's 22-footer, and the Suns led 30-26 after one.
A 10-2 spurt boosted the lead to 40-32 on Barbosa's driving layup.
The Suns outscored the Clippers 12-4 to start the second half, making it 79-59 on Richardson's 12-foot runner. Hill's three-point play on a rebound basket put Phoenix ahead 86-64.
Stoudemire's three-point play with 35.9 seconds left gave the Suns a 101-77 lead after three quarters.
"It's good for us to realize it's not about just showing up," Hill said, "it's about coming out and playing hard."
What was a strong stand to the Suns was a disappointing collapse for the Clippers.
"We just stopped playing," guard Baron Davis said. "We stopped hustling. We can't win if we don't hustle. With our athleticism, what we need on this team is hustle."
The Suns were 4-8 in Barbosa's absence. ... Nash is 18 shy of 14,000 career points. ... Phoenix has not lost three straight this season. ... After being outrebounded 14-1 to start the game, the Suns had a 44-26 advantage the rest of the way. ... Kaman had seven rebounds in the first five minutes and three the rest of the game.