Second-half goals from Theo Walcott and Michael Keane gave the Blues a 2-0 cushion before the hosts found their way back into the game with late goals through Josh King and Nathan Ake.
Walcott opened the scoring just before the hour mark, latching on to a perfectly-weighted through ball from Cenk Tosun and springing free of the Bournemouth backline.
The Blues doubled their lead ten minutes later as Keane headed home from a Gylfi Sigurdsson cross.
However, King cut into the lead after netting a penalty with 15 minutes to play before Ake bundled home from a corner to give the hosts a point.
Since Bournemouth were promoted to the Premier League in 2015, Everton have only won once on the South Coast - an FA Cup win - but they’ll have to return next season looking to find their first league win.
Richarlison and Smith see Red
Just before the half-time break, as Everton were beginning to grow into the game, Richarlison saw red after referee Lee Probert adjudged his and Adam Smith’s touching of heads to be violent conduct.
The Brazilian winger, unhappy with a tackle, turned to confront the Cherries defender and lent in, leading to the players being at nose to nose distance.
Richarlison turned his head, Smith threw his hands up and the Brazilian saw red.
However, Smith followed Richarlison down the tunnel in the second-half as he was issued a red for following Walcott as the last man before the eventual Everton goalscorer could get a free run into a one-on-one with Asmir Begovic.
Blues grow into game before the break
With the Blues growing into the game, the hosts had a glorious chance following an even better counter-attack. The Cherries broke down the left, worked they way into the Everton box before finding an unmarked Callum Wilson.
Despite composing himself, Wilson skied his effort into the stand behind the goal.
With little to write home about in the early goings of the half, the Blues begun to ramp up their pressure, springing attacks after jumping on loose play between the Cherries backline.
Walcott could have set away Tosun with one chance opted to go himself, running into danger and breaking down the attack.
However, it wasn’t all away pressure to close out the first period.
The Cherries caused trouble from a well-worked free-kick routine where Ake couldn’t get his head on the ball, instead, getting his shoulder on the delivery.
Yet, neither side could find a breakthrough during the first-half.
Keane stretched off to end proceedings
A wild second-half culminated as Everton’s trips to the Vitality Stadium do, with the hosts causing the Blues trouble.
Despite the action on the pitch, it was off the pitch that offered the biggest scare to Everton.
Keane, who doubled the Blues’ lead, collided with Idrissa Gueye as both players attempted to clear a high ball but the defender come off worst for wear - falling to the ground with little movement.
After a lengthy break, the defender was stretched off wearing an oxygen mask before stoppage time could be restarted.