The injury-hit Toffees were forced to play full back Tony Hibbert at centre half and were undone by Dmitri Likhtarovich's 16th-minute belter.
The BATE skipper unleashed a 30-yard thunderbolt which flew past Tim Howard to delight the home fans. It was a bitter pill to swallow for the Premier League side as Diniyar Bilyatedinov had earlier seen a superb shot cannon off a post.
Everton worked hard to continue their fine run of form but Cahill and Jo passed up opportunities to level the scores.
Aleksandr Povlov spurned a chance at the other end and a late rally proved decisive for David Moyes's Merseysiders.
First, Fellaini capitalised on some sloppy marking to direct a header into the net from Leon Osman's free-kick with 22 minutes remaining.
Then Cahill took centre stage by springing the offside trap to meet Bilyatedinov's header and slide to scoop an intelligent finish over Sergey Veremko.
"To go away from home and win in Europe is always tough," said Moyes.
"The conditions were not easy.
"But we're in a good position now and hopefully we can stay there and make it easier later in the group stages."
Everton top Group I in the Europa League with maximum points from two games, three points clear of AEK Athens and Benfica.
Please note: All comments are moderated.
Tick this box to accept our
TERMS & CONDITIONS
This article has 0 comments