A day after completing a blockbuster trade that sent leading scorer Jason Richardson and Hedo Turkoglu to the Orlando Magic, the Suns relied on their veteran mainstays to snap Oklahoma City's five-game winning streak.
Steve Nash had 20 points and 10 assists in his return from a neck injury that sidelined him for much of Friday's loss to the Dallas Mavericks, while new additions Vince Carter, Mickael Pietrus and Marcin Gortat, the three players acquired from the Magic, did not join the team.
Nash helped seal the win with two free throws that put Phoenix (13-13) up 112-109 with six seconds remaining.
After the teams traded foul shots, Oklahoma City forward Jeff Green missed a desperation shot from half court as time expired.
"Considering our circumstances tonight (being short-handed) we were really good tonight," Phoenix coach Alvin Gentry said. "Our defense was great, we shot the ball well, I thought it was a really good win."
The NBA's leading scorer, Kevin Durant, had 28 points for the Thunder, who fell to 19-9 on the season.
Russell Westbrook had 19 points and nine assists while Green also added 19 points for Oklahoma City, which staged a second-half comeback before falling short.
The Thunder trailed by 13 in the third quarter but used an 11-0 run to go ahead 85-82 heading into the fourth.
Phoenix tallied the first six points of the final quarter to take control and stayed hot while shooting 57 percent from the field for the game.
The 38-year-old Hill made nine of 17 shots from the field and 12 of 14 free throws to enjoy his first 30-point game since 2005.