Relegation rivals West Bromwich Albion and Cardiff City played out a six-goal thriller which saw both teams scored in stoppage-time.
Manchester United lifted some of the tension at Old Trafford with victory over Aston Villa, while Swansea City cruised to three points at home to Norwich City.
Southampton leapfrogged Newcastle United in the table after a convincing home win over Alan Pardew's side and Stoke City cemented their place in the top 10 by beating Hull City at home.
John Terry's second-half own goal condemned Chelsea to a shock 1-0 defeat at Crystal Palace to boost Tony Pulis' side's hopes of Premier League survival.
Palace took the lead seven minutes after half-time when Joel Ward's cross from the left was met at the near post by Terry and the Chelsea captain's touch glanced the ball past his own keeper Petr Cech.
Chelsea rallied as Eden Hazard forced an excellent save out of Julian Speroni, but Palace remained a threat at the opposite end as Cameron Jerome struck the post.
Manchester City missed out on the chance to take top spot after Arsenal came from a goal down to draw 1-1 at Emirates Stadium.
Manuel Pellegrini's side had the better of the first half and took the lead on 18 minutes when David Silva turned home the rebound after Edin Dzeko's shot had cracked back off the post.
But Arsenal improved after half-time and levelled on 53 minutes when, after moving the ball from right to left, Lukas Podolski's low cross into the box was swept home by Mathieu Flamini.
The result leaves City two points behind Chelsea, but with two games in hand, while Arsenal are five points adrift of the summit having played the same number of matches as the leaders.
Wayne Rooney scored a brace, and Juan Mata notched his first goal for Manchester United, as David Moyes' side came from a goal down to beat Aston Villa 4-1 at Old Trafford.
The build-up to the match had been dominated by talk of a planned protest and a plane carrying the message 'Wrong One - Moyes Out' flew over Old Trafford shortly after kick-off, although the fans inside the stadium showed their support by clapping the beleaguered manager as he took his place in the dugout.
While Moyes may have been buoyed by the reception from supporters at kick-off, his mood only deteriorated in the 13th minute when Rafael fouled Gabriel Agbonlahor just outside the box and Ashley Westwood curled an exquisite free-kick beyond the reach of David de Gea.
But United were level within seven minutes when Shinji Kagawa delivered a precise cross and Rooney barely had to move as he glanced a header into the bottom corner to relieve the tension.
Kagawa's defence-splitting pass led to United being awarded a penalty just before half-time when Mata was fouled by Leandro Bacuna and Rooney stroked a classy spot-kick deep into the corner.
United extended their lead in the 57th minute when Villa failed to clear after Marouane Fellaini struggled to fashion an opening, but Mata kept his cool to fire into the bottom corner from 12 yards to score his first goal since his January arrival from Chelsea.
There was still time for Javier Hernandez to put the icing on the cake for United, as he supplied a simple finish at the back post in the 90th minute after a great run and cross by fellow substitute Adnan Januzaj.
Mats Moller Daehli equalised in the fifth minute of added time as Cardiff salvaged a 3-3 draw at The Hawthorns just moments after West Brom had appeared to pinch the points.
West Brom took the lead after just two minutes when Gary Medel's poor header was seized upon by Morgan Amalfitano and his ambitious improvised effort from towards the right touchline looped over Cardiff keeper David Marshall.
It got even better for West Brom seven minutes later when a deflected cross found Matej Vydra at the far post and he cushioned the ball into the path of Graham Dorrans to finish from close range.
Cardiff pulled a goal back on the half-hour mark when Jordon Mutch, who scored twice against Liverpool last week, appeared to be trying to cross when his left-foot ball into the box curled beyond Ben Foster and inside the post.
The visitors equalised on 73 minutes when Medel swung in a deep free-kick and Steven Caulker's looping header had enough on it to beat Foster.
In the fourth minute of added time, West Brom looked to have won it when Saido Berahino's low cross was turned home at the near post by fellow substitute Thievy.
However, after West Brom had tried to catch Cardiff on the break, the hosts were rocked by a sucker-punch as Wilfried Zaha's low cross was teed up for Moller Daehli and his deflected shot span past Foster.
Swansea took a giant stride towards safety after Jonathan de Guzman's first-half brace set Garry Monk's side on the way to a 3-0 win over a toothless Norwich at the Liberty Stadium.
Norwich have struggled on the road this season and poor defending led to Swansea's opening goal when the visitors failed to clear and De Guzman drove home a low shot from the edge of the box on the half-hour mark.
De Guzman's second goal eight minutes later was pure quality as he rolled a pass into the feet of Wilfried Bony, whose clever back-heel played his team-mate into the box and the midfielder dinked a cute finish past John Ruddy.
Swansea further outlined their dominance on the game with 15 minutes to go when Jonjo Shelvey's pass teed up Wayne Routledge to fire into the bottom corner to move Monk's side seven points outside the bottom three.
Alan Pardew was back in the stadium, but it made no difference as the Newcastle manager watched his team thumped 4-0 by his former club Southampton at St Mary's.
Southampton missed a string of chances before taking the lead just before half-time when Rickie Lambert sprung the offside trap before squaring the ball for Jay Rodriguez to finish from close range.
The hosts doubled their lead four minutes into the second half when Adam Lallana clipped a pass towards the far post where Lambert was waiting unmarked to finish past Rob Elliot.
Lallana got in on the act with 20 minutes to go as, with Newcastle appealing for a free-kick which never came, the midfielder was allowed to run unchallenged before rocketing a left-foot shot from 25 yards past Elliot.
With a minute to go, Rodriguez scored his second of the game as a long pass over the top played in the England international and he finished confidently beyond Elliot.
Peter Odemwingie's second-half goal proved the difference as Stoke beat Hull City 1-0 in a tight contest at the Britannia Stadium to move Mark Hughes' side on to 40 points.
January signing Odemwingie struck in the 62nd minute when he fired in from the edge of the box after collecting the ball from a stray Ahmed Elmohamady pass to register his fourth goal in three games.