In the Toffees' first game since the Friedkin Group completed their long-awaited takeover, Sean Dyche's men were frustrating the Blues in the manner they frustrated Arsenal two weekends ago, with Jordan Pickford coming up trumps in terrible conditions.
The visitors' 76% possession in the first half but could not pick the Everton lock, and the hosts actually looked the more likely to score at the start of the second 45 before Chelsea regained a foothold in the game.
However, with Cole Palmer effectively being marked out of the game and Nicolas Jackson unable to get the better of Everton's centre-backs, Enzo Maresca's men were restricted to just the one point and were also indebted to Robert Sanchez and Tosin Adarabioyo for denying Everton a couple of gilt-edged chances too.
Chelsea have moved to within one point of Liverpool, but the Reds - who are now guaranteed to be top at Christmas - will go four clear should they overcome Tottenham Hotspur in the 4.30pm kickoff, while Everton rise up one place to 15th spot and now have a four-point buffer over the drop zone.
SPORTS MOLE'S VERDICT
Chelsea have already passed many stern tests of their title credentials over the past several weeks, but the Dyche defence examination proved a step too far for Maresca's men, just as it did for Arsenal a fortnight ago.
For the Blues, Sunday's game was a perfect opportunity to pile the pressure on the league leaders, who no doubt would have been aware of the result, but this will go down as one of their biggest opportunities missed so far.
Any superstitious Chelsea fans may not want to peek at this statistic; their side have won the Premier League title on all five occasions that they have been top at Christmas, but they have never finished first in the table when they have been second on December 25.
While Chelsea will consider Sunday's 0-0 as two points dropped rather than a point gained, a dogged Everton side should adopt the opposite mentality, even if they were also not starved of chances to nick a win on a positive first game for the new owners.
It is often still difficult to see where the next goal is going to come from for Everton, but their rearguard action is up there with the best in the country on its day, and not even the league's most dangerous attacking unit could break them down today.
MAN OF THE MATCH - TOSIN ADARABIOYO
Chelsea's offensive players may have lost their midas touch at Goodison Park, but Tosin Adarabioyo did not switch off at any point, and the Blues were arguably indebted to the former Fulham man for their point on Merseyside.
Iliman Ndiaye would have been wheeling away in celebration in the second half had Tosin not blocked his shot on the line, and the defender also made five clearances, two tackles and completed 92% of his passes.
Premier League starts have been hard to come by for Tosin in the current campaign, but the 27-year-old more than took his chance today and could give Maresca food for thought when Wesley Fofana is fit again.
EVERTON VS. CHELSEA MATCH STATS
Possession: Everton 25%-75% Chelsea
Shots: Everton 5-12 Chelsea
Shots on target: Everton 4-5 Chelsea
Corners: Everton 2-5 Chelsea
Fouls: Everton 20-12 Chelsea
BEST STAT
WHAT NEXT?
Sure to keep a close eye on Liverpool's blockbuster battle with Tottenham Hotspur on the coach home, Chelsea will be back in action on Boxing Day, hosting Fulham in a West London derby at Stamford Bridge.
A couple of hours before that all-capital affair, Everton actually have the honour of resuming the Premier League after Christmas; they will be in lunchtime action on December 26 away to champions-in-crisis Manchester City.
Written by
Ben Knapton