The Toffees drew 0-0 with the Blues at a wet and blustery Goodison Park on Sunday to extend their unbeaten run to three matches.
Robert Sanchez had a strong performance in the Chelsea net to deny Everton, with one close-range save against Jack Harrison a highlight.
However, Jordan Pickford also did his bit for the hosts to ensure they didn't concede in the difficult conditions.
Everton's clean sheet is their seventh in the Premier League since the beginning of October.
This is the most out of any club in Europe's top five leagues, including LaLiga, Serie A, the Bundesliga and Ligue 1.
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Furthermore, it's Everton's fifth clean sheet from their last six league fixtures, with a 4-0 defeat at Manchester United the only outlier.
Afterwards, Toffees boss Sean Dyche dismissed the sentiment that his side played an 'old school' style of football to earn their draw.
"There's no old school there, that's new school defending like that," he said to talkSPORT.
"Breaking passing lanes, breaking attacks, you can't do it now from old ways, you've got to do it with the modern tactical side and defending in our shape, working and being diligent to our shape.
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"I was very pleased with that again after a good performance at Arsenal from that side of things, and today we've opened up a little bit more and we've found chances.
"It would have been a tough one on them I think if we'd nicked it but we could've nicked, that can happen, and equally it would have been probably tough on us if they would have nicked it. So I think in the end, a point is about right for both teams today."
Dyche added: "We've formed a way of working, at times it's worked for us. Early season, we were out of them habits, we had to remind the players of them good habits and now we've lost two in 12.
"A lot of draws but clean sheets as well, seven in ten, I mean, these are good markers, they're good signs, not easy to do that in the Premier League.
"So a lot of what I'm looking at, certainly the will and desire and the effort of the players is intact. Now can we take it on again and then find that openness to our play and that cutting edge to our play?
"But against these sides, it's not easy you know, they defend well as well. It's not just about them keeping the ball, they defend well as well, so overall I'm pleased with the shift that the players put in again today."
Everton are four points clear of the relegation zone and have climbed to 15th in the Premier League with their draw against Chelsea.
They also have a game in hand following the postponed Merseyside derby against Liverpool earlier this month.