Everton captain James Tarkowski scored a dramatic stoppage-time equaliser as the Toffees fought back to earn a draw against Bournemouth at Vitality Stadium.
Alex Scott's first-half goal appeared set to give Marco Rose his first victory as Bournemouth manager, but Tarkowski struck in the 91st minute to deny the hosts all three points.
Everton had created the better opportunities during an entertaining opening period.
Jarrad Branthwaite saw an early header saved by Djordje Petrovic, while Thierno Barry was unable to convert the rebound after the Bournemouth goalkeeper had initially denied Tyrique George.
Despite Everton's chances, Bournemouth took the lead in the 41st minute.
Evanilson chased down a long pass, got the better of Tarkowski and found Scott on the edge of the penalty area, whose deflected effort beat the goalkeeper.
Everton almost responded immediately, but Barry could only find the side-netting following a quick counter-attack.
The striker went close again shortly after half-time, only for Petrovic to produce another important save from close range.
David Moyes' side then appealed for a penalty when Kiernan Dewsbury-Hall went down following contact with James Hill, but referee Chris Kavanagh waved away the protests.
Everton's persistence was eventually rewarded deep into stoppage time.
Marcus Tavernier and Ryan Christie failed to properly clear Hayden Hackney's corner, allowing Tarkowski to power home the loose ball and rescue a point.
For the second consecutive week, Rose saw his side concede late after appearing on course for victory.
Bournemouth had come close to giving their new manager a winning start against Manchester City before two late goals turned the match around.
This time, they at least collected their first point under the German, although the wait for his first victory continues.
Goalkeeper Petrovic was instrumental in keeping Bournemouth ahead for so long.
He produced an excellent stop from Branthwaite's header before turning Iliman Ndiaye's low effort behind.
Even after fumbling George's attempt, the Serbian recovered quickly enough to prevent Barry from converting the rebound.
Petrovic denied Barry again early in the second half, but his impressive resistance was finally broken by Tarkowski's late strike.
Rose faces a significant challenge after replacing Andoni Iraola, who guided Bournemouth to sixth place and Europa League qualification last season.
With a difficult trip to Newcastle coming next, Bournemouth's search for their first win under Rose continues.
Everton supporters entered the match with concerns extending beyond events on the pitch after Nottingham Forest submitted a £40m offer for highly rated midfielder Harrison Armstrong.
The 19-year-old is regarded as one of Everton's brightest academy prospects, and his future has become another major issue for Moyes ahead of the transfer deadline.
The Everton manager has already made clear that he wants additional signings before the window closes on 2 September.
Manchester City have also shown interest in attacking star Ndiaye, leaving Everton facing the possibility of having to defend interest in two important members of their squad.
Both Armstrong and Ndiaye started against Bournemouth, but Moyes will be eager to keep his key players while strengthening other areas of the squad.
After Everton finished 13th last season, the closing days of the transfer window could have a significant impact on their prospects for the campaign, with the club also continuing to search for reinforcements at right-back.
