Everton's poor start in the Europa League continued as they were held to a 2-2 draw at Goodison Park by Cypriot outfit Apollon Limassol, who finished the game with 10 men.
A fortnight on from the woeful 3-0 away defeat to Atalanta in their Group E opener, Everton fell behind in the 13th minute when Adrian Sardinero netted following a mistake by Ashley Williams.
Eight minutes later they capitalised on an error from Apollon's Hector Yuste, with Wayne Rooney stroking in his first European goal for Everton, and substitute Nikola Vlasic then opened his Toffees account by slotting home in the 66th minute.
That looked set to be the winner, but a chaotic finish to the contest saw the away side have Valentin Roberge sent off, then equalise moments later through Yuste's header, before Dominic Calvert-Lewin blew a superb opportunity to secure victory for the hosts at the death.
With Lyon and Atalanta drawing 1-1 in France in Thursday's other Group E match, Everton - who left the field at the end with boos ringing around the stadium - remain bottom of the pool.
With them needing to get points on the board in the group and looking to build on last week's wins over Sunderland in the Carabao Cup and Bournemouth in the Premier League, boss Ronald Koeman made only three changes to his starting line-up for this game.
But there was little rhythm to Everton's play in the opening stages - and then suddenly they were behind as Williams' blunder was punished.
Just outside his own area the defender gave the ball straight to Anton Maglica and - from his cross from the right - Sardinero hit a close-range shot that Jordan Pickford made a decent attempt to save but failed to prevent rolling over the line, with the Spaniard following up to make sure.
Everton still looked stunned moments later when Georgios Vasiliou cracked another effort at their goal that flew just off-target.
Soon after that, the home side had a major slice of luck come their way that allowed Rooney to bring things level.
Under pressure from Sandro Ramirez, Yuste botched a backpass to his goalkeeper Bruno Vale that Rooney intercepted with a simple finish - his first European goal for Everton.
It was a welcome boost for Rooney, for whom the previous week had not been the best, starting with his drink-driving conviction and the former England captain then being left with a cut above his left eye and a bloodied face on Saturday after being caught by the arm of Bournemouth's Simon Francis.
Rooney was grimacing again moments later, though, as he required more medical treatment. In the build-up to Gylfi Sigurdsson having a shot saved by Vale, Rooney miscued an attempt at an overhead kick and, having appeared to hurt himself when landing, he had to have his hand and wrist strapped up.
He initially seemed in considerable discomfort - it looked as if he took some painkillers on the touchline - but he was able to continue and curled a shot wide from just outside the box on the half-hour mark.
There was then another scare for Everton as Yuste put a header onto the roof of their net, before Tom Davies and Sigurdsson brought saves out of Vale in the last few moments of the first half.
Koeman brought on Vlasic for Idrissa Gueye at the interval and - after Pickford dealt with an Antonio Jokolis strike early in the second half - the change paid off. Rooney's pass ricocheted to Sigurdsson, and he fed Vlasic, who shot low past Vale.
If anything, it appeared Everton would then extend their lead, and Apollon's hopes looked particularly grim when ex-Sunderland man Roberge was dismissed in the 86th minute following a clash with Everton substitute Calvert-Lewin - but two minutes later Yuste headed in to make it 2-2.
Calvert-Lewin then had the goal at his mercy, but his close-range header was saved by Vale.