Manchester City regained the winning thread at Hull City, relegation rivals Sunderland and Crystal Palace played out a 0-0 draw, while Cardiff City suffered a last-gasp defeat away by Everton.
Norwich City remain in trouble after suffering defeat at Southampton and Stoke City moved above West Ham United in the table after beating Sam Allardyce's side at home.
Fabian Delph scored a stunning late goal as Aston Villa beat Chelsea 1-0 at home in a match which saw the leaders finish the game with nine men.
Chelsea saw a Nemanja Matic goal ruled out for handball just before half-time following a first half which was devoid of chances.
The Blues were reduced to 10 men on 68 minutes when Willian appeared to pick up a harsh second yellow card for a challenge on Karim El Ahmadi, having been booked for a foul on the Villa midfielder in the first half.
Villa struck decisively eight minutes from time when Delph superbly flicked the ball inside the far post from Marc Albrighton's pull-back after the former Leeds youngster had instigated the move.
Ramires was then rightly sent off in stoppage-time for a horrible tackle on El Ahmadi and Chelsea boss Jose Mourinho was then sent to the stands by referee Chris Foy.
Ashkan Dejagah scored a second-half goal to hand Felix Magath his first win as Fulham manager following a 1-0 success over Newcastle United at Craven Cottage.
Fulham thought they had taken the lead on 53 minutes when Johnny Heitinga's deflected shot from 25 yards struck the crossbar and bounced down, with the ball just catching enough of the line before rebounding off the bar again. Cauley Woodrow reacted quickest to the loose ball to score, but the young striker was ruled offside.
However, Fulham did take the lead on 68 minutes when Dejagah cut in from the left-hand side and his dipping 25-yard shot flew underneath Newcastle keeper Tim Krul.
Newcastle saw a late penalty appeal waved away as Fulham hung on for a welcome win, although Magath's side stay bottom of the table.
Under-pressure Pepe Mel finally celebrated his first win as West Brom boss after Youssouf Mulumbu scored a late winner to beat Swansea City 2-1 at the Liberty Stadium.
Swansea were quick out of the blocks and into a second minute lead after Wilfried Bony played in Roland Lamah down the left. The winger raced to the by-line and cut into the box before curling a low shot from a narrow angle inside the far post.
West Brom equalised on 52 minutes when Stephane Sessegnon lashed home a low shot from 25 yards after being teed up by James Morrison.
The Baggies then nabbed a winner five minutes from time when Mulumbu received possession around 40 yards from goal and was allowed to run unchecked before caressing a low shot from 25 yards beyond a rooted Michel Vorm.
Manchester City recovered from the early sending-off of Vincent Kompany to beat Hull City 2-0 at the KC Stadium to end the day six points behind Chelsea with three games in hand.
Captain Kompany was dismissed inside the opening 10 minutes after he hauled down Hull striker Nikica Jelavic 25 yards from goal, with the Belgian centre-half appearing to be hugely frustrated as he trudged off as he kicked the wall on his way through the tunnel.
The visitors responded to the setback in perfect fashion, though, as David Silva produced a moment of magic out of nowhere to break the deadlock on 13 minutes when he picked up a short pass from Yaya Toure and curled a sublime strike from distance into the top corner.
Manuel Pellegrini's side made certain of the points in the 90th minute when Silva's sumptuous outside-of-the-boot pass played in Edin Dzeko and the striker finished neatly past Allan McGregor.
Cardiff were denied a potentially important point at Goodison Park after Seamus Coleman's stoppage-time goal earned Everton a 2-1 win.
Everton grabbed the lead just before the hour mark when they worked the ball down the left-hand side before Gerard Deulofeu cut inside and his low shot took a deflection in beating David Marshall at his near post.
But Cardiff were level on 69 minutes when Peter Whittingham curled in a free-kick from the left and centre-half Juan Cala managed to help the ball over the line for his first goal for the club.
With Cardiff looking set to hold out, Everton snatched the points when Coleman's mis-cued volley looped over the line to lift Roberto Martinez's side up to sixth.
Sunderland remain in the bottom three after Gus Poyet's side were held to a 0-0 draw at home by fellow strugglers Crystal Palace.
Fabio Borini came closest to scoring when the on-loan Sunderland striker's shot cracked against the bar, while Kagisho Dikgacoi missed a late chance for Palace.
Southampton withstood a late rally from out-of-form Norwich to move up to eighth in the table on the back of a 4-2 triumph at St Mary's.
Southampton were in front after just five minutes when Gaston Ramirez's pass played Morgan Schneiderlin in on goal and the midfielder clipped his finish past John Ruddy.
Rickie Lambert made an immediate impact after being introduced as a substitute as he scored Southampton's second goal on 57 minutes, cleverly cutting inside a defender before placing his shot past Ruddy.
Lambert turned provider for Saints' third goal on 72 minutes as he teed up Jay Rodriguez to finish after Guly do Prado's shot had been saved.
Norwich pulled a goal back with five minutes to go when substitute Johan Elmander seized on a poor back-pass from Jose Fonte to finish past Artur Boruc.
And just a minute later, Norwich had scored a second when Southampton again conceded possession cheaply as Robert Snodgrass tucked away the loose ball after Boruc had pushed out Rick van Wolfswinkel's shot.
In added time, though, Southampton caught Norwich on the counter-attack and substitute Sam Gallagher notched his first Premier League goal after the visiting defence failed to prevent his shot from crossing the line.
Stoke came from behind to maintain their impressive home record this season with a 3-1 victory over West Ham United at the Britannia Stadium.
West Ham edged ahead in the fifth minute when Mark Noble chipped a free-kick into the box and Andy Carroll beat Asmir Begovic to the ball to head into an unguarded net.
Stoke levelled on 33 minutes when Peter Crouch's header from a corner came back off the crossbar and the giant striker acrobatically flicked a shot goalwards, with the ball deflecting in off team-mate Peter Odemwingie.
Kevin Nolan had a goal disallowed for West Ham for offside before Stoke took the lead on 69 minutes when Marko Arnautovic enjoyed a lucky bobble of the ball following a neat build-up before rolling his shot past Adrian.
The Potters wrapped up the points on 79 minutes thanks to a quick break as Stephen Ireland played in Odemwingie and the January signing's shot rocketed into the top corner.