However, Fernando Torres netted his first league goal of 2013 with 15 minutes left to play to give Chelsea the points.
Sports Mole takes a closer look at the action from the Bridge.
On target 10
On target 9
Was the result fair?
Just about, although a draw would not have been an injustice. Both sides showed no fear going forward as they gave the fans an entertaining 90 minutes. However, the hosts were just that bit more clinical in front of goal as they managed to wrap up the points.
There was plenty of flair up front from the Blues, but there was also some questionable defending at the back. That said, the match proved how fit the squad is following their Europa League exploits in midweek.
Manager David Moyes is sure to be happy with the commitment from his players in what was his last game in charge. On more than one occasion they had Chelsea pinned back in their own half, but poor finishing mixed with a lack of concentration late on cost them a share of the spoils.
Sports Mole's man of the match
Juan Mata: The Spaniard capped a fine season with a superb display from midfield. Once he had opened the scoring he was involved in all of Chelsea's attacks, often leading his teammates from the front.
Tim Howard will be disappointed with Chelsea's opening goal after spilling Demba Ba's tame shot to allow Juan Mata to tap in. The American has been rock solid for Everton this season and it is a shame that this happened in the final game of the campaign.
There were a few tasty tackles flying in during the encounter but Anthony Taylor remained calm throughout the 90 minutes. He allowed play to flow more often than not which contributed to an entertaining match.
Chelsea: The Blues will now head out to the USA, where they face Manchester City in two friendlies before the end of the month.
Everton: The Toffees will begin their search for a new manager as they will lose David Moyes to Manchester United this summer.