Their smart start to the season had led to thoughts the Goodison outfit might just challenge for a first title in 31 years.
But the Merseyside Blues were off-colour against the Blues of London and were well and truly put in their place by the Stamford Bridge outfit.
Ronald Koeman and his men had excuses for a display which saw the champions cruise to victory - with goals from Spaniards Cesc Fabregas and Alvaro Morara - without getting anywhere near their best.
It was their third away match in less than seven days, following Monday’s 1-1 draw at Manchester City and an identical result in the Europa League in Croatia against Hajduk Split on Thursday.
But if Koeman and Co want to be among the big boys, they’ll have to learn fast how to handle the domestic-Euro conundrum much, much better than this.
The closest they came to a shot on target was in the 87th minute when Idrissa Gueye’s rising effort was tipped over by Thibaut Courtois, even though it probably wasn’t going in.
Earlier Sandro scuffed a shot which hit Antonio Rudiger and went for a corner - following Rooney’s best pass of the match - but that was not going in either.
Rooney, who surprisingly wore a full-length base layer under his shirt despite the sun scorching down, was hot under the collar much of the match, eventually getting booked for dissent by ref Jon Moss in the 71st minute.
Against a team who twice tried to sign him, the former England star must have realised yesterday that things aren’t as good as he at first thought at Goodison - having scored his team’s only two league goals so far this season to earn them four points.
He never looked like adding to that tally, finding himself the target for abuse a minute before his caution when he miscued a volley horribly wide.
As for Chelsea and their boss Antonio Contre, they must have loved this stroll in the sun.
But with Everton being so poor, failing to add any goals in the last 50 minutes of the match show they have a long way to go before they start entertaining thoughts of retaining their title.
It was a good day for Morata, though, as he continued to adapt to life in the Premier League by scoring the second and setting up the first.
An interchange with Fabregas in the 27th minute saw him cushion a clever header into his countryman’s path, with the midfielder stroking in at the far post with the outside of his right boot.
Thirteen minutes later Morata glanced home a header - the provider this time being a third Spaniard, with Cesar Azpilicueta crossing.
Chelsea could and should have scored more, with Pedro and Victor Moses in particular failing to make the most of opportunities.
And having drawn Atletico Madrid and Roma - as well as having to tackle a difficult trip to face Qarabag in Azerbaijan - the west Londoners, who were out of Europe when they won the title, will soon be facing a test of their own resources.
This week promises to be interesting for both Conte and Koeman as they try to persuade the powers-that-be at their respective clubs to buy the players they say they need to fight on two fronts.
