Successive 0-0 home draws have not done much for Claudio Ranieri's future or anything much to secure second place in the Premiership for Chelsea.
With Manchester United losing earlier in the day, Chelsea had a golden opportunity to put clear daylight between themselves and the Red Devils.
But goal-shy Chelsea had only two Frank Lampard long-range efforts to cheer, both times the ball hitting the Everton woodwork.
Everton for their part were content to frustrate Chelsea and hope for something on the break.
They did their homework and came away with a deserved point.
It started brightly for Chelsea with a thundering challenge by Robert Huth in first minute signalling his intent.
A quick throw-in by James McFadden almost caught the home side out as Tomasz Radzinski beat Wayne Bridge, but the striker's cross was well held by Marco Ambrosio.
On five minutes, a deep Alessandro Pistone cross was met by Radzinski's unmarked header from just outside the penalty area, but it went harmlessly wide.
Chelsea should have taken the lead on seven minutes when a long ball from Ambrosio was headed on by Jimmy Floyd Hasselbaink into the path of Adrian Mutu, but the Romanian's attempted chip did not cause Nigel Martyn any problems.
After ten minutes Mutu set up Hasselbaink beautifully, but the Dutchman's powerful was well off target sailing into row Z of the Shed.
A minute later Joe Cole needlessly upended Pistone. Wayne Rooney whipped the resulting free-kick around the wall, forcing Ambrosio to parry. The home side then broke quickly but Martyn was able to cut out a Geremi cross to quell the danger.
The dangerous Geremi then set-up Hasselbaink but the out of sorts Dutchman fell over as he tried to make contact and the ball rolled harmlessly to safety.
The Blues were desperately unlucky not to score after 24 minutes after excellent work by Scott Parker, who fed Lampard. The former West Ham star turned and shot in one quick movement from the edge of the penalty area, but the ball clipped the crossbar and bounced harmlessly wide.
On 30 minutes a Geremi corner picked out Mutu, but the Romanian's header flew over the Everton crossbar from six yards out.
Two minutes later Ambrosio pulled off a brilliant save with his legs from a Rooney shot to keep the scores level, before Huth blocked another effort from the England striker, whose influence was growing by the minute.
On the stroke of half-time Huth miscalculated a ball into the penalty area allowing Rooney to nip in behind him and get a shot in on target, but Ambrosio was more aware than his defender and was quick to get down and block.
It was left to hot-shot Hasselbaink to liven up the home spectators with a blistering 25-yard screamer which Martyn did well to punch clear.
Chelsea started the second half quickly but not could capitalise on an early corner, before Gary Naysmith upended Cole on the edge of the penalty area after 51 minutes.
But Huth, who has a powerful shot, blasted his effort straight into the wall and the danger was cleared.
Everton boss David Moyes replaced McFadden with Lee Carsley in an attempt to stem Chelsea's attacking moves, but the move made little difference and almost immediately Mutu fired wide when well placed.
Most of Chelsea's attacks fell apart on the edge of the Everton area, and once behind the Toffees rearguard, no one was in place to provide the killer touch.
With not much happening on the pitch, Moyes decides to shake up his charges, by bringing on Francis Jeffers after 78 minutes for Radzinski.
Ranieri countered this with a double substitution of his own, with Jesper Gronkjaer and Filipe Oliveira coming on for Joe Cole and Scott Parker.
Within 60 seconds Hasselbaink teed up Mutu but somehow he managed to head wide.
Oliveira got in some nice early touches but it was Lampard's left-footer in the 82nd minute that took the plaudits, crashing against Martyn's left upright.
Late Chelsea pressure saw them force two corners, while Hasselbaink was unfortunate to see a cross from Mutu bounce off his knee. But in untruth the Londoners were destined not to score and the pressure continues to mount on Ranieri.
With former Ajax and Barcelona coach Louis Van Gaal in the stands watching the match at chief executive Peter Kenyon's invitation, the intense speculation about Ranieri's future will inevitably continue.
Afterwards Ranieri admitted: "It was a strange match, but sometimes we could have lost this game. We tried to do the right things, and were very focussed. We needed three vital points, but there are excuses." The Italian also revealed that he has an injury crisis looming before Tuesday's Champions League semi-final first leg away to AS Monaco.
"John Terry has an ankle problem," he said. "I hope that Damien Duff, Eidur Gudjohnsen, Hernan Crespo and Claude Makelele recover from their sickness, but I will find out tomorrow when we train." Everton boss David Moyes was more than happy with the point. "I played with three forwards," said the Scotsman.
"I hoped that we might get something against a good Chelsea side. We tried to stiffen up our performance but in the main, we had to defend for long periods.
"We are not mathematically safe from relegation yet, but we have had two very good away performances recently." He admitted that he took a leaf out of Middlesbrough's book. "I saw them get a 0-0 here and tried to copy them and it worked," he confirmed.
Man of the Match: Frank Lampard tried his best to open up Everton, but on this occasion, the England midfielder could not raise the standards of his team-mates to better things.