Ross Barkley looked to have wrapped up the win for Everton by scoring within five minutes of added time, but Stanislas headed home on the stroke of full time to earn the Cherries a point.
Below, Sports Mole has dissected the extraordinary events on the South Coast.
On target: 10
On target: 6
Was the result fair?
Very much so! Had Bournemouth come away with nothing from this afternoon's game, then it would have been a very cruel outcome. The cliche of 'a game of two halves' rings true on this occasion as Everton completely dominated the first half, exploiting Bournemouth's defensive woes and easing to a 2-0 lead before the stroke of half time.
Eddie Howe made a change in the interval by hauling off defender Steve Cook and replacing him with Smith, who played at right-back, therefore allowing Simon Francis to move into a centre-back role. That change was crucial to the Cherries' dynamic in the second half as they took control of possession and showed desire to get back in the game.
They looked to be dead and buried after 80 minutes, but a wonder-goal from Smith and Stanislas's strike got them on level terms. It was a sickening blow to Bournemouth when Barkley scored in added time as Everton did not deserve to earn all three points, but Stanislas was there again to score and rightfully award Bournemouth a point.
Manager Eddie Howe has said many times that he will not change his team's open, attacking style of play, despite the side showing defensive frailties in recent matches. It seemed to be the same old story for Bournemouth this afternoon when Everton took advantage of some poor defending to score twice in the first half.
Funes Mori's opening goal came too easily as he did not even need to rise much in the box to get a header on target, and the second goal was poor marking from Cook as he was on the wrong side of the Belgian before he struck past goalkeeper Adam Federici.
Injury concerns mounted for Bournemouth as Federici was replaced at half time after landing awkwardly on his ankle while defending a corner, but the arrival of Smith changed everything for the hosts. He provided an additional attacking threat and scored a wonderful goal to reduce Everton's lead.
The Cherries were boosted by the strike and then took control of the game. At times, it was frustrating for the team as their attempts just were not coming off, but they showed that they never give up as Stanislas managed to equalise twice.
Roberto Martinez's side took some time to find their stride, but they managed to do so and after the first 10 minutes of the match, they were in complete control of the match. There were plenty of spaces for the likes of Lukaku and Gerard Deulofeu to run into, and after taking a 2-0 lead, the team went into cruise control almost.
Bournemouth did not pose much of a threat to the Toffees during the first 45 minutes, and because of that, Everton seemed to be far too relaxed in the second half. They acted as if the game was already won and it was dangerous for them as they seemed content to sit back and play on the counter-attack.
Everton were punished for their approach in the second half as they lost their two-goal lead. Even though Barkley scored what seemed to be the winner at the time, which caused the travelling supporters to spill out onto the pitch, it would not have been a deserved win for the Merseyside outfit.
Sports Mole's man of the match
ADAM SMITH: Stanislas may have scored the two crucial goals for Bournemouth, but it was Smith's introduction in the second half that changed the game for the home side. The right-back used his pace to get forward and his curling effort from outside the box to reduce the deficit inspired the team fight back and earn an all-important point.
Before Bournemouth got themselves back into the game, the team's defensive errors would have been mentioned in this section, but the biggest blunder across the 90-plus minutes was Everton's apparent complacency in the second half. They dominated up until the half-time whistle and had a comfortable 2-0 lead, but they rested on that after the break as opposed to trying to wrap the game up. Perhaps they underestimated Bournemouth's ability to get back into the game.
Kevin Friend was not warmly received by the home supporters due to some contentious decisions, both involving Smith. In the second half, Brendan Galloway looked to have been clipped by Smith, but the right-back played on as the assistant did not flag. However, Friend blew his whistle for the foul, causing outrage among the fans. Later in the half, Smith went to ground in the box after tussling with Galloway, but penalty shouts were denied.
BOURNEMOUTH: The Cherries will face Chelsea for a Premier League clash at Stamford Bridge on Saturday, December 5.
EVERTON: The Toffees will take on Middlesbrough in the quarter-finals of the Capital One Cup on Tuesday, December 1. body check tags ::