The 36-year-old Hill, often written off because of a series of serious injuries over his 14-year NBA career, scored 26 points, including a tiebreaking jumper in the lane with 31.5 seconds remaining, to lift the Phoenix Suns to their season-high sixth straight victory, 118-114 over the Utah Jazz on Wednesday night.
The Suns remained three games behind the Dallas Mavericks in their push for the eighth and final playof spot in the Western Conference. Each team has 11 games left, with one game between the teams April 5 at Dallas.
The Jazz dropped 1 1/2 games behind the first-place Denver Nuggets in the Northwest Division.
Hill, the Suns' leading scorer for the second straight game -- he had 23 points Monday night against Denver -- is the only Suns player to play in all of the team's 71 games this season. He has revived his game under coach Alvin Gentry, who replaced Terry Porter just after the All-Star break.
Jokingly referring to his age, the affable Hill said, "I watched the movie 'Cocoon' last week." The film is about a group of older people.
Gentry said he is "biased" when talking about Hill.
"I've known him since he was 15," the coach said. "I coached him in Detroit. Everyone should have an opportunity to coach a player like him. I've been lucky. I've been able to coach him twice.
"He's playing as good as when he was 25. The big thing is he's healthy. He's made a lot of big plays for us."
The score was tied at 114 when Hill made his critical fadeaway 9-foot shot. After Utah missed two field goal attempts, Barnes completed the scoring with two free throws.
Utah now is 0-9 on the road against Western Conference playoff teams, and 14-21 overall away from home.
Utah coach Jerry Sloan was unhappy with the officiating and his team's foul shooting.
"I thought Paul Millsap got fouled under the basket," Sloan said about a missed field-goal attempt in the closing seconds. "Those are things for the officials.
"And when you shoot free throws like that [16-for-27] in a game like this, that's the ball game. It makes it very difficult. Plus, we gave up too many points in the paint. They scored 68 points in the paint, and I don't know when any team has scored so many points in the paint against us."
"Fastbreak points, that's where all the points in the paint came from." Boozer said.
Utah had only 38 points in the paint. The Suns also outscored the Jazz 31-14 on fastbreak points.
The Jazz trailed for most of the first half, but used an 18-6 spurt over the final 6 minutes of the second quarter to seize a 58-52 halftime advantage. Williams, with six points, and Kirilenko, with five, sparked the Jazz's late run.
Williams finished the half with 13 points and Boozer had 12 points and nine rebounds for the Jazz. Richardson, who hit his first six shots, led the Suns with 15 and Hill had 14.
Utah, which generally plays a slowdown half-court game, showed no hesitation in running with the fast-breaking Suns, moving the ball upcourt crisply and efficiently. They also converted eight offensive rebounds into 11 points and hit five 3-pointers. On the defensive end, they often double-teamed O'Neal and limited him to four shots and five points, and held Nash to six points on 2-for-7 shooting.
Each team had a big run in the third quarter. The Suns, spurred by nine points by Barnes, opened with a 15-4 burst and took a 67-64 lead. The Jazz responded with an 11-4 spree, capped by a 3-pointer by Kyle Korver, and regained the advantage, 73-71. Utah extended its margin to 78-71 before the Suns had the final run, 18-5, and led 89-83 entering the fourth period.
Nash's ninth assist of the game and the 7,393rd of his career, enabled him to pass Maurice Cheeks for ninth place on the NBA's all-time list. ... Utah has had a total of 142 games missed because of injuries; last year the Jazz had only 42. ... The Jazz's top three scorers -- Williams, Boozer and Okur -- didn't appear in the same game this season until Feb. 23. ... Phoenix is 7-0 against sub-.500 teams under Gentry. ... The Suns are the only team in the league shooting better than 50 percent from the field. ... Bart Starr, the former Green Bay Packers' Hall of Fame quarterback, was a courtside spectator.