Jason Thompson added 15 points and Beno Udrih made a big 3-pointer in the closing minutes to help the Kings win their third straight.
The Sixers were led by Jrue Holiday's 28 points, while Jodie Meeks added 22. Philadelphia missed a chance against one of the NBA's worst teams to make up ground on fifth-place Atlanta.
"We are fighting to make the playoffs. Sacramento is playing with house money," Collins said. "Hopefully, we learned. We have a lot of work to do. This was not a good day."
There were crackles of excitement, notably Lou Williams' 32-foot 3-pointer at the buzzer that sent the game into overtime, and Holiday's 16-point fourth-quarter, but the Sixers lost at home to a team that won just its 20th game of the season.
The Kings trailed by five at halftime, but Thornton's 19-point third quarter helped get them out of the hole. Trailing 91-87 with 4:58 to play, Holiday scored the next nine points for the Sixers -- capped by a 3-pointer -- to put Philadelphia up 96-91 with 2 minutes left.
Sacramento quickly tied it again after Thornton drilled a jumper, then a 3-pointer with 36.6 seconds to play.
In the closing seconds of regulation, Udrih made two free throws to give Sacramento a three-point lead, then the team opted not to foul Williams before he shot, and barely guarded him as he went up.
"We should have fouled Lou, but we didn't," Dalembert said.
The Kings outscored the Sixers 8-2 in the closing minutes of overtime, including Dalembert's free throws with 12 seconds to play that gave Sacramento a four-point lead. As he ran down the court to boos, he kissed his lips and pointed to the sky. The center, who spent his first eight NBA seasons in Philadelphia, finished with 13 points and 19 rebounds.
The Kings won for the first time in six overtime games.
"We could've easily folded the tent [because of] how things were going out there," Thornton said. "But, you know, hats off to our guys. We stayed in there and came out with a huge win."
After making 12 of their first 21 shots, the Sixers made 28 of 69 the rest of the game. Their bench was worse, shooting 4 for 26 (15 percent) and scoring just 14 points.
The Sixers (37-36) have lost two straight and are 4-6 in their last 10 after completing a 16-5 stretch. The Kings owned the boards, outrebounding Philadelphia 58-36 one game after Miami had a 49-31 rebounding edge against the Sixers.
"They're huge," Collins said. "There's no question. Elton [Brand] had three rebounds in 39 minutes. Evan [Turner] had one in 20 minutes. Thad [Young] had one in 18."
Overall, it wasn't a good finishing effort.
"I knew Sacramento was playing a lot better basketball than the last time we played them," Collins said. "They can score and make it very difficult for you to score. We got off to a good start. I thought it was fool's gold from moment one, and I told our guys that. We lost an edge. We never got it back, and then we fought and almost stole the game."
The Kings stole it back in overtime.
"Our team has a tendency to hang our heads and not bounce back from those kinds of things," Kings head coach Paul Westphal said. "We haven't been a good closing team for most of the year, but lately, we've improved in that area, too. We found a way to score, but mostly we stayed in the game because of our defense and rebounding."
Evans played in his second game since missing the previous 19 with left foot plantar fasciitis, scoring 10 points in 23 minutes. ... The Kings have won four of their past five after winning four of the previous 22 games.