Stoke goalkeeper Asmir Begovic came to the rescue numerous times for the visitors and prevented an even heavier scoreline.
Below, Sports Mole has looked back over the 90 minutes that unfolded and whether the result was deserved.
On target 12
On target 3
Was the result fair?
It's very rare for a team to score four goals and finish the match undeserved winners, so yes, Everton were right to take home the three points this afternoon. From the first whistle, the Toffees' display was of a higher quality that their opponents, and they showed why they have been so impressive at Goodison Park this season. After Deulofeu gave them the lead just before half time, Martinez's men went from strength to strength after the break. Had Begovic not been in fine form, Everton could have scored many more.
Once again, it was a strong team performance from the home side as they pulled together some impressive passages of play. The midfield was the most vital part of the pitch, and Everton controlled it throughout the entire game, with Leon Osman especially playing through his attacking teammates. Despite being without Leighton Baines, Bryan Oviedo looked comfortable as left-back and even added a goal to his performance this afternoon.
Stoke City's performance
The Potters' approach to the game started off well as they were able to close Everton down and defend when needed. However, they began to lose their grip on the encounter as the minutes went on and Everton piled on the pressure. It took around half an hour for the away side to have a shot on goal, and it was scuffed by Jonathan Walters, which summed up their afternoon.
Sports Mole's man of the match
Leon Osman: He may not have been one of the four goalscorers, who are likely to get the headlines, but Osman rarely put a foot wrong in midfield throughout the match. The 32-year-old's movement and passing gave the attacking players ahead of him the freedom to get in dangerous positions. He also prevented Stoke from getting a stronghold in the middle of the park.
With Stoke rarely getting any chance in front of goal, any opportunity that came about needed to be latched on, but this was not quite the case for Brek Shea. Erik Pieters played the ball across goal as Shea drove into the box, but the midfielder failed to get a foot onto it and should have done a lot better.
There were a few incidents that Mike Jones had to contend with, and some Everton fans may feel that they could have had a penalty following three shouts, which were all dismissed by the match official. In the first half, Steven N'Zonzi should have been cautioned after wrapping his arm around Steven Pienaar's neck, but Jones waved away the incident.
Everton: The Merseyside outfit take on Premier League champions Manchester United at Old Trafford next Wednesday.
Stoke City: The Potters play host to Cardiff City at the Britannia Stadium on December 4.