Nikola Vlasic netted his maiden Goodison goal but a last gasp equaliser robbed Everton of their first win in this season’s Europa League group phase.
In a frustrating encounter, the Blues - like they had done against Bournemouth in the Premier League on Saturday - looked to have picked up victory having gone behind.
Adrian Sardinero put the visitors ahead on 12 minutes but first Wayne Rooney then Vlasic seemingly saw the points stay in England.
But Hector Yuste guided a header past Jordan Pickford to snatch two of those points away at the death.
Everton went into the match again missing centre-half duo Phil Jagielka and Michael Keane through injury, while Jonjoe Kenny was rewarded for his impressive cameo from the bench against Bournemouth with a start. Dominic Calvert-Lewin was named amongst the substitutes, with Sandro Ramirez selected alongside Wayne Rooney in attack. Saturday’s hero Oumar Niasse watched from the stands due to his non-inclusion in the Club’s Europa League squad for the group stages.
Apollon arrived on Merseyside on the back of a 1-1 home draw with Lyon in the first round of fixtures a fortnight earlier - and they were followed on the journey from Cyprus by around 800 noisy, partisan supporters.
They had eliminated FC Zaria Balti, Aberdeen and FC Mitjylland en route to reaching the group stage, showing that despite playing in a country ranked 70 in the FIFA World ratings, they were not to be underestimated.
This point was underlined with a quarter of an hour played when the visitors took an early lead. Anton Maglica found space down the right channel and he played across a pinpoint centre which was converted by Sardinero at the second time of asking.
Apollon then went close to doubling their advantage in the next attack, as captain Georgios Vasiliou flashed a left-foot shot just past the post.
Everton soon regained parity, though, through Rooney who capitalised on a terrible defensive lapse from Yuste five minutes later. The defender received a short goal-kick and instead of clearing his lines, opted to play it back blindly to keeper Bruno Vale. It was wide of the mark, Rooney nipped in and had the simplest task of prodding home from just a few yards out.
That leveller sparked Everton into life and a low save from Vale denied Gylfi Sigurdsson from scoring with an acrobatic attempt.
Rooney, nursing an apparent injury to his wrist, then curled narrowly wide from outside the area, as did Sandro Ramirez who was still looking for his first competitive Everton goal.
Everton peppered the Apollon goal in the closing moments of the first half and Vale made two necessary stops in quick succession, firstly beating away a cleanly-struck drive from Tom Davies and then positioning himself well to thwart Sigurdsson with a 20-yard free-kick.
Ronald Koeman made an attack-minded change at the break, replacing holding midfielder Idrissa Gana Gueye for the more adventurous Vlasic, who was making just his fourth appearance since his deadline day move from Hajduk Split.
The Croatian took up an old-fashioned inside-left role, and he weaved in from that position 10 minutes into the second half, only to drag a shot wide of the post.
Rooney fired high into the Gwladys Street not long after and, despite Everton’s domination in possession, a fiercely-struck long-range effort from Antonio Jakolis, which required careful attention from Pickford, served as a warning sign of Apollon’s capabilities on the counter.
It was only a matter of time before Everton nudged ahead and the Blues’ second of the evening duly arrived on 65 minutes though Vlasic.
Sigurdsson played a perfectly-weighted slide-rule pass for the 19-year-old who raced clear and netted with composure to open his account, a month after completing his switch from the Croatian top division.
Dominic Calvert-Lewin was introduced by Koeman straight after the Blues had taken the lead and he was only an inch or two from ensuring Everton won by a greater margin with a curling shot from outside the box which flew past the post by the closest of margins.
Limassol were reduced to 10 men late on when Roberge was handed a straight red card for a stamp on Calvert-Lewin.
Despite their numerical disadvantage the visitors managed to find a late, late leveller. A deep free-kick from the left found Yuste and he guided it past Pickford.
Within minutes, Calvert-Lewin had a glorious chance to regain the lead - Vlasic picking him out from the left - but the striker’s downward header was stopped by keeper Vale.
It proved decisive, with the final whistle sounding soon after, with Everton pushing until the final seconds to find a late winner.
Heartbreaking for the Blues, who have little time to dwell on the disappointment - Burnley visit Goodison Park on Sunday.