Chelsea surrendered a halftime lead to lose 3-1 at West Ham United to leave interim manager Rafael Benitez still without a win and Arsene Wenger was also the target of jeers as his Arsenal side were humbled 2-0 at home by Swansea City.
Champions Manchester City moved top of the Premier League table, for a couple of hours at least, after Carlos Tevez earned them a 1-1 draw at home to Everton, although Manchester United will open a three-point lead if they win at Reading later.
Juan Mata gave Chelsea a well-deserved lead but West Ham roared back to pile pressure on Benitez with former Chelsea striker Carlton Cole levelling just past the hour before substitutes Mohamed Diame and Modibo Maiga struck late on.
Benitez, whose appointment in the wake of Roberto Di Matteo's sacking has proved unpopular among fans, is the first Chelsea manager not to win any of his first three matches in charge since Russian oligarch Roman Abramovich bought the club.
"In the second half we didn't start well, they got on top of us and we couldn't manage," former Liverpool manager Benitez, whose first two matches in charge ended in 0-0 draws against Manchester City and Fulham, told Sky Sports.
The European champions, now without a win in seven league matches having topped the table, remain in third spot on goal difference from Tottenham Hotspur, who joined them on 26 points with a 3-0 victory at Fulham -- Jermain Defoe scoring twice.
West Bromwich Albion slipped to fifth, also on 26 points, after a 1-0 defeat at home by Stoke City.
Arsenal were booed off at the Emirates as they slipped to 10th following Michu's late double for Michael Laudrup's impressive Swansea, which took the 2 million pound summer signing's tally for the season to 11.
"Of course you can understand the fans when we lose a match the way we did today," Wenger told Sky Sports.
"We were maybe lacking a bit of maturity to keep it 0-0. It's a big blow because the games are coming very quickly. Today was not the way we want to play football."
Liverpool were 1-0 winners at home to Southampton and bottom club Queens Park Rangers drew 1-1 at home to Aston Villa as their search for a first league win of the season continues under new manager Harry Redknapp.
Banners protesting about Benitez's appointment were still in evidence at Upton Park, yet for 45 minutes Chelsea were in control and heading for victory.
When Fernando Torres cut the ball back from the byline for Mata to shoot Chelsea in front after 13 minutes, it seemed that Benitez could silence his critics, at least for a day.
Mata could have increased Chelsea's lead but Jussi Jaaskelainen made a great save to keep West Ham within touching distance.
West Ham's Kevin Nolan had a goal disallowed just before halftime and Chelsea keeper Petr Cech made a fingertip save to keep out Nolan's header from a corner.
The home side were far more adventurous after the break and deservedly drew level when Cole nodded past Cech from close range after appearing to climb over Branislav Ivanovic.
Mata nearly restored Chelsea's lead with a superb free kick that thudded against the woodwork and Chelsea looked the more likely winners as the game entered its closing stages.
However, West Ham, who had not beaten Chelsea for nine years, roused themselves for a final surge.
Ashley Cole had to head Winston Reid's header off the line, and with four minutes of normal time remaining Diame smashed a low shot past Cech.
Disgruntled Chelsea fans were already heading for the exit when Maiga converted a rebound for the third after Cech had saved Matt Taylor's shot.
Manchester City extended their unbeaten league run at home to 37 matches but they were given a scare when Marouane Fellaini scored for Everton after 37 minutes.
Argentine Tevez levelled just before halftime when Fellaini was adjudged to have dragged down Edin Dzeko.
"If teams come here and get soft penalties awarded against them it's going to be hard to get a result," Everton manager David Moyes told Sky Sports after his sixth-placed side's eighth draw in 15 league games.
Which team will win the 2013/14 Champions League?