"It wasn't pretty, especially early on," Dudley said. "It's been two games at home where we haven't gotten it going early but defense kept us in there."
Channing Frye was emblematic of both the Suns' offensive struggles and defensive success, shooting 2-of-18 from the floor but adding a key free throw. He pulled down 14 rebounds and held Blake Griffin to 17 points on a season-low 6 of 19 from the floor.
"He bodied him up and played with him, and 6-for-19 is as good as you can hope from him," Suns coach Alvin Gentry said. "The great thing is we took everything away from him."
Chris Paul had 16 points and Kenyon Martin added 14 off the bench for the Clippers, who shot 37 percent en route to their second loss in their past three.
"I felt like we were really dead and didn't have it," Griffin said. "There was not a lot of energy. There's no excuse."
The Suns, who trailed by 11 points midway through the second quarter, opened a 63-52 lead on Markieff Morris' 3-pointer with 9.7 seconds left in the third.
The Clippers slowly rallied, tying the game at 70 on Mo Williams' 3-pointer from the left corner with four minutes to play.
Gortat blocked Caron Butler and Frye made 1 of 2 free throws to give the Suns a 77-72 lead with 29.5 seconds left. Paul pulled the Clippers within 77-75 with a wide-open 3-pointer from the top of the arc off the inbounds pass with 26.5 to go.
After a pair of Phoenix timeouts, Frye broke free to Hill's inbounds pass before the Suns worked the ball to Dudley, who was fouled. Dudley's two free throws put the Suns ahead, 79-75.
Paul attempted a 3-pointer but his shot was blocked by Hill, who then scored on a layup to secure the Suns' 13th win in their past 14 games against the Clippers.
"We shot horribly," Hill said. "We had good looks. We had great shots. They just didn't go through or go in. For the most part, our defense sustained."
Phoenix scored just 15 second-quarter points -- barely outpacing the Clippers' 14 -- yet trailed only 35-32 at the half. Hill gave the Suns their first lead since the early minutes, 38-37, on 14-foot jumper 9:56 into the third quarter.
"We just didn't shoot it," said Clippers coach Vinny Del Negro. "Both teams played last night. They struggled shooting. We struggled shooting. It was a low-scoring, ugly game especially in the first half."
The Suns have won nine straight at home against the Clippers, dating to April 17, 2007.
The Suns' field goal percentage was their lowest in a win since Nov. 1, 2002 against Cleveland, when Phoenix shot 33.3 percent. ... Frye missed his first 10 shots, all in the first half, before scoring on a dunk 23 seconds into the second half. His other field goal was a 3-pointer, after which he stuck out his tongue and pumped his fist as he ran up the court. ... Los Angeles shot 35.7 percent from the floor in the first half, the Suns 29.5 percent. Missed shots were so prevalent that after Hill missed a second-quarter free throw, Clippers C DeAndre Jordan, Griffin and Frye all handled and squeezed the ball in turn, as if making sure it wasn't a foreign object. ... Gentry is 10-1 against the Clippers, whom he coached from 2000 to 2003. ... The Suns' 32 first-half points were a season low. ... Terrell Owens and Evander Holyfield were in attendance ahead of a celebrity basketball game Saturday.