Willian hit a last-minute winner to beat Everton 1-0 to keep the Blues seven points clear of Manchester City at the top of the league.
Chelsea seemed to have run out of ideas having peppered the visitors goal for much of the match.
Also if it wasn't for Petr Cech, the Blues may have lost the game as the stopper produced the save of the match in the second half to thwart Romelu Lukaku.
With a draw looming William tried his luck from range and his 25-harder took the slightest of deflections off Steven Naismith on its way past Tim Howard.
This was Chelsea's game in terms of possession, but Everton can count themselves unlucky that their defending failed to produce the point they deserved.
Nemanja Matic tried his luck from 25 yards after two minutes and his effort inched over Tim Howard's crossbar.
This was quickly followed by a sizzling Willian right-footer that echoed Matic's.
Ex-Chelsea striker Romelu Lukaku forced Petr Cech into a last-ditch stretch of his left leg to turn the Belgian hit man's shot away for a corner as the opening 10 minutes became a game of 'No, you shoot first.'
Chelsea should have had a penalty on four minutes when Steven Naismith inexplicably lobbed the ball into the air with upper part of his right arm in the Everton penalty area. Referee Jonathan Moss either did. It see it or chose not to do anything about it. Either way Jose Mourinho was fuming in the dugout at the decision.
Howard was finally called into proper action, grabbing Loic Remy's towering header away from the goal line on 13 minutes.
Eden Hazard just failed to connect to a Cesar Azpilicueta and Remy again shot the ball across Howard's goal as the home side struggled to find the killer touch.
Hazard was next up to test Howard on 32 minutes and the midfielder's daisy-cutter from the edge of the penalty area was well held by the USA stopper.
Everton boss Roberto Martinez made one change at half time, replacing liability Mohamed Besic with James McCarthy.
Jose Mourinho opted to his his misfiring front men an opportunity to make amends.
Seamus Coleman was on hand to kick away a Hazard byline cross just as Willian was about to pounce at the far post as the Blues surged forwards in waves in an effort to break the deadlock.
Howard parried away a Hazard shot on 62 minutes.
The goalkeeper was in action a minute later, tipping round his left post, a curling free-kick from Matic.
Then he stretched to parry away a Willian right-footer.
On 69 minutes, Sleepy Chelsea almost conceded when Bryan Oviedo centred from the left. john a Terry and Kurt Zouma missed the movement of the ball and Lukaklu got a close-range touch on it. Incredibly Cech somehow kicked out his left boot and deflected the ball away from goal.
Mourinho had seen enough and replaced Remy and Juan Cuadrado with Didier Drogba and Cesc Fabgrgas..
A zipper of a 25-harder by substitute Mirallas threatened Cech's goal with 12 minutes left on the clock.
Chelsea thought they had scored through a deflected Matic shot, but the ball hit Ivanovic who was in an office position. Sixty seconds later and with two minutes left and Gareth Barry received a second yellow card for fouling Willian.
A melee ensured which seem to see Ivanovic lock heads with James McCarthy.
Then dramatically, Willian arrowed a pile driver towards goal. It took slightest of nicks off Naismith. But enough to send the ball past Howard to put the Blues ahead.
Teams: Chelsea, Cech,Ivanovic, Zouma, Ramires, Hazard, Remy Matic, Willian, Cuadrado, Terry, Aolicueta
Subs, Courtois, Luis, Fabregas, Ake, Drogba, Cahill, Loftus-Cheek
Everton, Howard, Jagielka, Oviedo, Lukaku, Naismith, Besic, Barry, Barkley, Coleman, Lennon, Stones
subs, Robles, Gibson, Kone, Mirallas, McCarthy, Garbutt, Alcaraz
Referee Jonathan Moss