John Terry's scrambled goal, in the 93rd minute of the game, kept Chelsea ahead of the pack in the title race
Below are five lessons learned from the result:
Eden Hazard needs more help as he shoulders the attacking burden for Chelsea
Despite some nice flicks and touches from the likes of Samuel Etoo and Willian, Eden Hazard was very much the man expected to, and comfortable trying to, break the deadlock in what would go on to be a tight contest.
As Oscar's form has tailed off a little in recent weeks, Eden Hazard has only become a more integral part of this Chelsea team, and it is abundantly clear that the Belgian needs someone else to step up to shoulder some of the burden for the Blues.
At the moment, opponents will feel that if you stop Hazard, you go a long way to stopping the whole team, and this is a chance for another to really ensure their importance to Jose Mourinho's side.
Thibaut Courtois will do well to oust Petr Cech
There are few goalkeepers that have have such an excellent record when it comes to making saves after having nothing to do for the majority of the game.
Petr Cech has played behind the tightest Premier League defence of the last ten years, and much of his work is in having to maintain outstanding levels of concentration to stay alert to the few strikes decent enough to find their way through.
Against Everton, Cech made two wonderful stops from the lively Leon Osman, and it will be a tough ask for Thibaut Courtois, who this week Jose Mourinho said would be back at Chelsea next year to challenge Cech for the number 1 jersey, to take the Czech's place.
Azpilicueta is fast becoming one of the best fullbacks in the league
The young Spaniard played again from the left hand side for Chelsea, but was happy mopping up on the right too, wherever his pace and concentration was needed, and was excellent for the entire game.
After displacing Ashley Cole in the Chelsea side, a man many considered the best left back around, Azpilicueta has gone from strength to strength, and considering he isn't even playing on his favoured flank, he has to be considered one of the league's best, and most versatile fullbacks.
This was a vital result, potentially a title winning one
It looked like being another frustrating afternoon for Chelsea, as Everton defended resolutely and battled well for a share of the spoils.
That was until Frank Lampard's wonderful free kick that dropped somewhere between John Terry and Tim Howard. As it nestled in the net, the stadium erupted and it felt like a pivotal moment in the title race.
If Chelsea would have drawn after the disappointing result at West Brom, that superb win at the Etihad would have almost been wasted. Now, Chelsea move ahead at the top of the league, incapable of being captured by anyone this weekend.
There is something special about this home Chelsea record
The win made it an incredible 74 league games unbeaten at home for Chelsea when they have Jose Mourinho in charge.
It emphasises the special connection between the manager, club, players and fans, and is surely one of the great records in modern football. At times, Chelsea have ridden their luck to avoid defeat, but "you make your own luck" as the old saying goes, and whatever your thoughts on the Portuguese, it's impossible to dismiss it.
Who knows when it will end, or what will happen once it does.
image: © Ben Sutherland