Yerry Mina struck a 99th-minute equaliser to earn Everton a 1-1 draw and a dramatic point against Wolves in their mission for Premier League survival.
Despite a bright start, the Blues were dealt a blow when Nathan Patterson was forced to withdraw through injury just before the half-hour mark, then, 11 minutes before the interval, Hwang Hee-Chan swept home the opening goal for the hosts.
There was more pain for Everton on the stroke of half-time, as Dominic Calvert-Lewin limped off with another injury setback.
It looked as though that might be the end of the story, until Mina prodded home from close range in the final minute of second half stoppage time to earn a share of the spoils at Molineux.
Sean Dyche made one change from the side defeated at Manchester City, with Amadou Onana recalled to the starting line-up in place of Mason Holgate.
Question marks, then, as to how Everton would shape up with an extra midfielder - and it would be Dwight McNeil who would deputise in an unfamiliar left-back role, with Alex Iwobi offering protection on the left of midfield, as Dyche opted to stick a tried-and-tested 4-5-1 formation from the start.
The message from the 3,010 travelling Evertonians taking up the entire length of the Steve Bull stand ahead of kick off was simple, with a large banner displaying the words 'FIGHT FOR US' held up as the teams appeared from the tunnel.
Determined to play the role of awkward visitors again, the Toffees - unbeaten in their past three away games heading into this one - once again won the coin toss and turned the teams around ahead of kick off.
It was Everton who looked by far the more threatening side in the opening exchanges.
With less than five minutes on the clock, Mina cushioned a header from McNeil's free-kick into the path of Calvert-Lewin, who swivelled and rattled the side netting with a rasping left-footed strike.
Half chances continued to fall the way of the Blues' number 9, as he headed wide from Doucoure's cross from the left before nodding an effort off target from Alex Iwobi's centre from the same flank following a sweeping counter-attacking move started by captain Jordan Pickford in goal.
Everton remained on top until an injury to Patterson - sustained in a fair challenge on Daniel Podence - forced the Scotland international off, with Michael Keane his replacement at right-back.
Six minutes later and completely against the run of play, Wolves took the lead.
Winning back possession midway inside his own half, Adama Traore drove forward and forced an excellent save from Pickford with a low drive from the edge of the penalty area - but, unfortunately for Everton, the rebound fell straight to the feet of Hee-Chan, who completed the simplest of tasks by tapping the ball into an empty net from close range.
Undeterred, Everton came forward again and were presented a chance to get back on level terms almost immediately when Calvert-Lewin was brought down 25 yards from goal.
The impressive James Garner was the man to take it, but his effort flashed over the crossbar.
Calvert-Lewin's withdrawal as the first half drew to a close compounded a miserable end to an opening period that began positively.
Wolves had kept clean sheets in all nine of their Premier League home wins this campaign and only Manchester United can better their overall tally of 10.
In a bid to break that stubborn defence, Dyche switched to a 3-5-2 system for the second half, with James Garner switched to right wing-back.
Alex Iwobi threatened with a well-struck left-footed shot that was well held by Daniel Bentley.
Wolves responded with a flurry of chances.
First, Pablo Sarabia curled a shot wide of Pickford's right-hand post, before Nelson Semedo smashed a shot wide following Podence's clever reverse pass, then Podence volleyed wide a chance of his own moments later.
Everton remained on the hunt for an equaliser, though, and went close when Demarai Gray - Calvert-Lewin's replacement - stung the palms of the Wolves goalkeeper with a rasping strike after working himself a yard to beat Toti in the left channel.
As the Toffees continued to push for a leveller, Pickford was on hand to produce a superb stop with his feet to deny substitute Matheus Nunes on a breakaway.
Then, in the final minute of added time, a delivery into the penalty area was nodded down by James Tarkowski, squared by Michael Keane and poked home by Mina to send the travelling Evertonians into raptures.
It means the race for Premier League safety will go down to the final day of the season, with Everton set to host Bournemouth at Goodison Park on Sunday 28 May (4.30pm BST).