Even with 10 males, after a overdue sending-off, Apollon struck for an 88th minute equaliser when Hector Yuste headed in a loose-kick.
Everton sub Nikola Vlasic concept he had delivered the winner within the 66th minute, completing clinically after Wayne Rooney benefitted from a lucky jump off a defender, Gylfi Sigurdsson taking part in in his teenage crew-mate.
Rooney had previous equalised together with his 3rd objective of the season for the Toffees nevertheless it used to be every other a long way from convincing efficiency from the large-spending crew Merseyside membership.
After struggling a humbling three-zero defeat at Italian side Atalanta of their opening crew recreation, Ronald Koeman desperately wanted a win to kick get started their European marketing campaign.
But the sport used to be handiest 12 mins outdated when Koeman noticed a horrible defensive slip by Ashley Williams present the guests the opener.
There used to be no power at the Welsh world as he seemed to care for a stray thru ball.
Williams cleared the ball without delay to Anton Maglica and his go discovered Spanish ahead Adrian Sardinero who scored at the second one try after Jordan Pickford blocked his preliminary, shut-vary shot.
And Everton had been similarly lucky as a deficient Mason Holgate clearance allowed Georgios Vasiliou a shot from 30 yards that whistled simply extensive.
It used to be a being concerned get started for the Toffees, who have been required to come back from at the back of to overcome Bournemouth on Saturday.
But thankfully for Koeman, Apollon had been simply as shaky in defence as his side and passed Rooney the equaliser within the 21st minute.
Full-back Yuste, beneath power from Sandro, hit an terrible again go that flew previous keeper Bruno Vale and allowed Rooney to stroll it into an empty objective.
It used to be simply the fortunate spoil Everton had wanted, relieving the power and including momentum to their attacking play.
Four mins later, Jonjoe Kenny’s go noticed Rooney, proper, swing and omit with Sigurdsson hooking the free ball instantly at the keeper.
Rooney additionally suffered a hand damage in that transfer, after a defender by chance stamped on it, and the previous England captain used to be obviously in ache as he won remedy and returned with the wrist closely strapped.
Rooney then curled a shot narrowly extensive at the part-hour after patience and robust play by Williams unfolded the customer’s defence.
But the Cypriots proved they nonetheless posed a risk when defender Yuste rose smartly to move Joao Pedro’s nook onto the roof of the Everton objective.
Davies, with a company shot from open play, and Sigurdsson, with a an identical effort from a 20- backyard loose-kick, examined the keeper.
Koeman threw on ahead Vlasic at part-time and there used to be slightly extra pace about Everton’s play.
Rooney virtually performed in Sigurdsson, with Vale hurrying over to hide, however there have been nonetheless considerations in defence the place Antonio Jakolis used to be allowed a long way an excessive amount of area and his 25-yard strike compelled Pickford right into a diving save.
Apollon’s Valentin Roberge used to be despatched off within the last phases for stamping at the again of sub Dominic Calvert-Lewin after which Yuste surprised Goodison together with his overdue leveller.