However, one club not struggling near the top of the table are Liverpool, who climbed into second as In-form striker Luis Suarez scored once again in a 4-1 romp over West Ham at Anfield to climb into second behind league leader Arsenal.
MORE: Manchester United's Premier League crisis | Tottenham make it two straight with Sunderland win
An own-goal from Guy Demel put Brendan Rodgers' side in front just before half-time before France defender Mamadou Sakho scored his first Liverpool goal just after the break.
Martin Skrtel's own goal gave West Ham hope, but Suarez struck 10 minutes from time for his 14th league goal of the season.
The Uruguayan's shot then deflected in off Joey O'Brien to seal Liverpool's fifth successive home win, a run in which they have scored 20 goals.
West Ham, now 17th on the table and above the relegation zone on goal difference alone, also had skipper Kevin Nolan sent off for a late challenge on Jordan Henderson as their wait for a first win at Anfield for 50 years continues.
Kevin Nolan of West Ham United is shown a red card by Referee Michael Oliver during the Barclays Premier League match between Liverpool and West Ham United at Anfield. Photo by Clive Brunskill/Getty Images
Oussama Assaidi, meanwhile, proved the hero as his spectacular long-range effort helped Stoke City (12th) snatch all three points in the final minute to secure a 3-2 victory over third-placed Chelsea.
Jose Mourinho's first visit to the Britannia Stadium got off to the perfect start thanks to Andre Schurrle's ninth-minute opener, but two goals either side of half-time from the hosts put them ahead.
Peter Crouch and Stephen Ireland netted for Mark Hughes' side but their lead was soon wiped out as Schurrle grabbed his second in the 53rd minute.
However, Chelsea were not able to hold onto the point as Assaidi fired a sensational effort into the top corner from 25 yards to record a memorable victory.
Ramires of Chelsea in action with Glenn Whelan of Stoke during the Barclays Premier League match between Stoke City and Chelsea at Britannia Stadium. Photo by Scott Heavey/Getty Images
Assaidi won't be the only player making the highlights reel on Saturday as Pablo Daniel Osvaldo netted a sumptuous strike to earn Southampton (eighth) a 1-1 draw in a pulsating encounter with Manchester City (fourth).
The fiery Italy international was involved in an unseemly post-match melee as Southampton slipped to a third consecutive defeat amid an injury crisis against Aston Villa last Wednesday, but he returned to St Mary's Stadium and grabbed the headlines for the right reasons in this encounter.
A superb individual effort from the big-money close-season signing was the least Mauricio Pochettino's team deserved in a match they dominated for long periods after Sergio Aguero continued his purple patch in front of goal in the 10th minute.
Manuel Pellegrini's City won at West Brom last Wednesday, but this was a display far more in tune with the away-day woes that threaten to derail their Premier League title bid.
Pablo Daniel Osvaldo of Southampton shoots to score the equalising goal during the Barclays Premier League match between Southampton and Manchester City at St Mary's Stadium. Photo by Bryn Lennon/Getty Images
Last-placed Sunderland's poor week for own goals continued as John O'Shea scored down the wrong end of the pitch to help Tottenham (sixth) come from behind for a 2-1 victory at the Stadium of Light.
The hosts took the lead late in the first half when Adam Johnson capitalised on a Hugo Lloris error following an Ondrej Celustka cross.
But Tottenham were level before the break through Paulinho before O'Shea inadvertently diverted the ball past Vito Mannone in the 50th minute to hand the visitors all three points.
Jermain Defoe was also twice denied by the woodwork as Tottenham went in search of a third.
Defeat for Sunderland – a result that leaves them bottom of the Premier League and without a win in four – will be especially difficult to stomach as a Phil Bardsley own goal handed Chelsea a 4-3 win at the same ground on Wednesday.
Paulinho of Tottenham shoots past Vito Mannone, Goalkeeper of Sunderland for his goal during the Barclays Premier League match between Sunderland and Tottenham Hotspur at the Stadium of Light. Photo by Jan Kruger/Getty Images
David Moyes' woes continued as Manchester United (ninth) were beaten at home for the second time in four days, losing 1-0 to Newcastle United (seventh).
The Premier League title holders lost 1-0 against Moyes' former club Everton on Wednesday and were beaten again on Saturday by a Newcastle side who picked up their first away league win at Old Trafford since 1972.
Yohan Cabaye was the man on target for Newcastle, with the France international scoring after an hour.
He calmly finished inside the area after being played in well by Moussa Sissoko to inflict consecutive home league defeats on the hosts for the first time since 2002.
Alan Pardew's side had a slice of luck, however, as Vurnon Anita looked to handball an effort off the line at 0-0, before Robin van Persie saw what would have been an equalising goal ruled out for offside.
Patrice Evra of Manchester United and Moussa Sissoko of Newcastle compete for the ball during the Barclays Premier League match between Manchester United and Newcastle United at Old Trafford. Photo by Richard Heathcote/Getty Images
Goals from Gary Hooper and Leroy Fer saw Norwich City (14th) end a run of four away league defeats with a 2-0 win at West Brom (15th) on Saturday.
Hooper's 13th-minute strike - his second goal in three matches - and Fer's last-minute goal ended a wretched run of results on the road for Chris Hughton's side, who had conceded 18 goals in those four defeats and were absolutely humiliated by the Luis Suarez show in last Wednesday's 5-1 loss to Liverpool.
The ex-Celtic forward took his goal well, sending a finish across Boaz Myhill after being set up by Fer, before the Dutchman made the game safe in the final minute, cutting inside from the left to shoot low into the net.
West Brom had thrown on Shane Long and Saido Berahino for the second half but the hosts, and Stephane Sessegnon in particular, were guilty of wasting chances to bring themselves back into the game.
Norwich player Leroy Fer celebrates after scoring the second goal with Gary Hooper and Josh Murphy during the Barclays Premier League match between West Bromwich Albion and Norwich City at The Hawthorns. Photo by Stu Forster/Getty Images
Lastly, Cameron Jerome haunted his former club as Crystal Palace (18th) recorded a valuable 2-0 Premier League victory over Cardiff City (16th) on Saturday.
The striker – on loan from Stoke City – opened his account for the Selhurst Park club with a headed effort six minutes in.
Marouane Chamakh then scored his second goal in as many matches to double the hosts' lead after the interval, as Palace's resurgence under new manager Tony Pulis continued.
The result gives Palace their first back-to-back league victories of the season, while Cardiff are winless in five.
Cameron Jerome of Crystal Palace and Steven Caulker of Cardiff City challenge for the ball during the Barclays Premier League match between Crystal Palace and Cardiff City at Selhurst Park. Photo by Jamie McDonald/Getty Images