The win was the Suns' eighth in 10 games and gave them a four-game season sweep of the Kings.
It was the second consecutive game the Suns held an opponent under 90 points, a rarity for a team known for its offense but notorious for its poor defense.
On Friday night, the Suns limited Atlanta to 30 points in the second half. Against the Kings, they allowed only 34 points after intermission, including only 15 in the third quarter, a season low for a Suns opponent.
"Defense and rebounding, that's what we did in the beginning of the season." Richardson said. "We got away from that for a while. But now guys are taking it upon themselves to do what we were doing in the beginning of the season. I think when we defend like that we are tough to stop."
The Suns also outrebounded the Kings 49-38, including grabbing 20 offensive boards.
Stoudemire admits that he now is finally starting to grasp the finer points of defense.
"In college is where you learn the fundamentals of defense but I didn't go to college," he said. "When I played with Team USA, defense was important. Now, I'm starting to enjoy it."
Coach Alvin Gentry was especially pleased with the Suns defense.
"I thought we did a great job," Gentry said. "I thought Steve did a good job on Tyreke Evans. We probably did the best job we've ever done as far as dribble penetration. I thought our defense was the difference."
The Kings began the season 9-8, but since then they are 9-30. They are 5-25 on the road and have lost nine straight in Phoenix.
Grant Hill added 16 points and Nash scored 11 for the Suns, who are 13-0 when holding an opponent under 100 points.
The Suns (34-23) are 11 games over .500 for the first time since opening the season 14-3.
Despite playing the second night of a back-to-back, the Kings were sharp at the outset. They moved the ball crisply, hit 56.1 percent of their field goal attempts and racked up a Suns-like 16 fast-break points.
"We weren't good enough to play 48 minutes of the kind of basketball you need to beat Phoenix in Phoenix," Sacramento coach Paul Westphal said. "We couldn't keep them off the offensive boards which hasn't been a problem for us all year but has been the last two games."
Evans admired the work of Stoudemire on the boards.
"He's a beast," Evans said. "He was coming in there, jumping over everybody, snatching the rebounds and putting them back up. That's what hurt us. We've got to do a better job of holding them to one shot, like they did to us."
Greene, who burned the Suns for a career-high 31 points on Feb. 5 but failed to score Saturday night against the Los Angeles Clippers, led the balanced Kings offense with 11 points at halftime.
The Kings led by 10 points midway through the second period and 54-51 at halftime.
Richardson scored 19 points in the first half and Nash, playing despite a troublesome abdominal strain, already had 10 assists at the break.
The Kings began to wear down in the third quarter and the Suns capitalized. Phoenix held Sacramento to 15 points in the period, when the Kings made only five of 15 shots, and the Suns surged ahead 75-69. Stoudemire was the spark, scoring seven points and grabbing nine rebounds.
The Suns took control by opening the fourth quarter with seven straight points, five by Channing Frye, and the Kings never seriously threatened again.
Evans is trying to become the fourth player in NBA history to average 20 points, five rebounds and five assists in his rookie season. Before Sunday's game, he was averaging 20.3 points, 4.9 rebounds and 5.3 assists. The only players who have accomplished that are Michael Jordan, LeBron James and Oscar Robertson. ... Stoudemire's 19 points ended his streak of at least 20 points in nine straight games.