Everton were reduced to nine players as Wolverhampton Wanderers continued their recent improvement, with exciting teenager Mateus Mane’s strike giving them a point at Hill Dickinson Stadium.
Michael Keane and Jack Grealish were both sent off in a chaotic conclusion which saw bottom club Wolves, surely doomed to relegation, almost snatch victory at the death.
Everton led from the 17th minute when defender Keane pounced from close range for his third Premier League goal of the season.
But Wolves, who secured their first league win of the season at the 20th time of asking against West Ham United, boast a new resilience under manager Rob Edwards and stayed in contention until teenage forward Mane made another decisive contribution with 21 minutes left.
The 18-year-old, who scored his first senior goal in the 3-0 victory over the Hammers, showed great composure to run on to substitute Jorgen Strand Larsen’s pass and beat Everton keeper Jordan Pickford.
There was little hint of the drama and chaos to follow in what had been a largely undistinguished game until tempers boiled over in the closing stages.
Keane’s night turned sour with seven minutes left when he was shown a straight red card after a lengthy video assistant referee (VAR) intervention following an aerial clash with Tolu Arokodare, where the defender looked to have pulled the hair of the Wolves striker.
Grealish then followed him down the tunnel after picking up a second caution for dissent – both coming in the space of three minutes – to leave Everton to see out a nervy nine minutes of additional time.
Wolves almost snatched victory, only for Pickford to produce a magnificent save from Hugo Bueno’s long-range effort.
Everton’s fans reacted furiously at the conclusion of a game that was low on quality but suddenly became high on drama late on.
It was a mixture of anger at the dismissals of Keane and Grealish, but also a large measure of disappointment at another toothless, lacklustre display.
Keane was adjudged to have tugged at Arokodare’s hair as they both went up for a header, while Grealish sarcastically applauded and continued to argue with referee Tom Kirk after already receiving a yellow card in the 87th minute, inviting the fate the eventually came his way.
It was reckless ill-discipline on Everton’s part that almost cost them the point they were clinging to following a good start.
Attempting to bounce back from a heavy 4-2 loss at home to Brentford, David Moyes’ side led through Keane’s goal, but then barely threatened Wolves keeper Jose Sa and ended up hanging on desperately with a numerical disadvantage.
Moyes has struggled with a lack of attacking threat all season, but the situation has reached desperation with Iliman Ndiaye away at the Africa Cup of Nations with Senegal and Kiernan Dewsbury-Hall out with a hamstring injury.
Everton and Moyes would have hoped to use their fine win at Nottingham Forest as a springboard to move up the table, but one point from two home games against Brentford and now Wolves is a poor return for the 12th-placed side.
Wolves manager Edwards looked disappointed at the final whistle after his side could not capitalise on Everton being reduced to nine men.
He must have thought Bueno’s spectacular late strike had brought the riches of a second successive league win, only for Everton keeper Pickford to pull off a world-class save.
Edwards, however, will be delighted the recent improvement – that saw Wolves push Arsenal and Liverpool close before disappointing defeats, land a draw at Manchester United and then get that elusive first league win of the campaign against West Ham – was maintained.
Heads could have dropped after going behind so early, but there is fresh determination about Wolves now under his charge.
With a 14-point gap to fourth-bottom Nottingham Forest, it would take the stuff of miracles for them to avoid the drop, but there is no doubt there has been progress in recent weeks.
This has been exemplified by the exciting Mane with another demonstration of his talent, and this time producing an ice-cool equaliser.
Brought in as an academy player from Rochdale, the England Under-18 international has emerged as a welcome positive in a troubled season for the club – although his form will have already caught the attention of potential transfer suitors.
Everton face Sunderland in the FA Cup third round at Hill Dickinson Stadium on Saturday, 10 January (12:15 GMT). They then travel to Aston Villa in the Premier League on Sunday, 18 January (16:30 GMT).
Wolves are home to Shrewsbury Town in the FA Cup third round on Saturday (12:15 GMT), before Rob Edwards’ side host Newcastle United at Molineux on Sunday, 18 January (14:00 GMT).
