Junior Stanislas scored a 98th-minute equaliser as Bournemouth twice came from behind to earn a point in an astonishing game at Vitality Stadium.
Everton looked set for victory when goals from Ramiro Funes Mori and Romelu Lukaku put them 2-0 up at half-time.
Adam Smith rifled in a sizzling strike from 25 yards and Stanislas converted Joshua King's cut-back to make it 2-2.
Ross Barkley swept a shot in on the turn in the 95th minute but Bournemouth responded through Stanislas's header.
Only five minutes of added time had been signalled, but in truth few could begrudge Bournemouth their last-gasp equaliser after a hugely spirited second-half display.
They remain in the relegation zone but move up one place to 18th, while Everton remain seventh after twice squandering winning positions.