West Ham came from behind to beat Chelsea 3-1 and leave the European champions without a win in seven league matches, three since Benitez replaced the fired Roberto Di Matteo as manager.
Chelsea remains third but Tottenham is now only behind on goal difference in fourth place after beating Fulham 3-0.
Arsenal dropped to 10th after Michu's double gave Swansea a 2-0 victory at Emirates Stadium.
Man City temporarily regained top spot despite being held to a 1-1 draw by Everton. But Manchester United could return to the summit by winning at Reading in the late match Saturday.
Queens Park Rangers remains winless and bottom after being held to a 1-1 draw by Aston Villa, while West Bromwich Albion dropped to fifth after being beaten 1-0 by Stoke and Liverpool defeated Southampton 1-0.
Liverpool's former manager, Benitez, is enduring a miserable return to the league he left in 2010 with the fans against him and the team not performing.
Chelsea took the lead at West Ham in the 13th minute when Fernando Torres cut the ball back from the right to Juan Mata, who swept in his eighth goal of the season.
The hosts fought back in the second half, with former Chelsea striker Carlton Cole equalizing in the 63rd minute after taking the place of the injured Andy Carroll.
Cole set up Mohamed Diame's decisive goal for West Ham in the 86th before being replaced by Modibo Maiga, who added a third in stoppage time.
"We could have finished the game in the first half, but it was totally different in the second half," Benitez said. "We didn't start well, they were on top of us and we couldn't manage ... we gave the ball away easily, weren't comfortable in possession."
And the fans made their opposition to Benitez clear with "Rafa Out" banners and chants backing Di Matteo.
At Arsenal, manager Arsene Wenger also faced jeers from his own fans and the team's title hopes faded further.
Swansea went in front in the 88th when Michu broke free after a neat one-two with Luke Moore and slotted the ball into the net.
In stoppage time, the Spaniard latched onto a long clearance and raced through to again beat goalkeeper Wojciech Szczesny, prolonging Arsenal's worst start to a league season since Wenger arrived in 1996.
North London rival Tottenham is buoyant after a third win on the run. Sandro put Spurs ahead 10 minutes into the second half with a 35-yard strike, before Jermain Defoe scored twice in five minutes.
At Etihad Stadium, Marouane Fellaini headed Everton in front in the 33rd, but managed to concede a penalty before halftime after tangling with Edin Dzeko.
That allowed Carlos Tevez to equalize from the penalty spot and preserve City's unbeaten start to the season.
Liverpool recorded only its second win in seven league matches after Daniel Agger headed in his first goal of the season just before halftime against relegation-threatened Southampton.Suggest a correction