BATE 1 - 2 Everton
Tim Cahill popped up with a vital goal to earn a makeshift Everton a hugely creditable Europa League Group I win over Belarussian side BATE in Minsk.
The Australian latched on to Diniyar Bilyaletdinov's flick-on to lob home expertly late on and reward a manful performance from the Merseysiders.
The hosts had gone ahead when Dmitri Likhtarovich smashed in from 35 yards.
But Marouane Fellaini headed home his first of the season to draw Everton level before Cahill sealed the victory.
The result makes it two wins from two for David Moyes's side in Europe, but this was a far more taxing three points than the 4-0 defeat of AEK Athens at Goodison Park a fortnight ago.
Moyes had warned his side beforehand not to take the Belarusian side lightly, and a look at their results in last season's Champions League group stages told its own story.
Two draws against Juventus and another at Zenit St Petersburg underlined they are no pushovers and already this season BATE are firmly on course to secure a fourth straight league title.
And Everton's cause was not helped by the absence of 10 first-teamers, with Joseph Yobo pulling out of the squad late on Wednesday with a thigh injury to join the likes of Phil Neville, Steven Pienaar and Phil Jagielka on the sidelines.
Still, the Merseysiders were far from out-matched in a keenly-contested first half which saw only Likhtarovich's wonder striker separate the sides.
Only moments before the midfielder's pile-driver, the impressive Bilyaletdinov crashed a left-footed shot against the post from 16 yards out after linking up well with Yakubu.
And Cahill, too, almost made the most of a good opportunity, Jo and Yakubu combining to free the midfielder in the box, only for the Australian to badly scuff his shot as the chance went awry.
But apart from the goal, BATE failed to really test Toffees keeper Tim Howard at all in the opening period - despite causing stand-in right-back Dan Gosling all sort of problems.
However, the second half saw the hosts further impress their passing game on the Toffees, and Aleksandr Pavlov and Sergei Krivets both could have done better when the ball fell to them in the box.
Everton's backline held firm manfully, though - particularly stand-in centre-half Tony Hibbert - and one of their defensive heroes Leighton Baines then turned provider up the other end to deservedly draw them level.
The left-back swung over a beautiful cross and Fellaini - completely unmarked at the back post - nodded a simple header down and past stranded keeper Sergei Veremko.
Suddenly, the Toffees believed they could go on and win, and the poacher supreme Cahill dutifully stepped up to the mark with 77 minutes on the clock.
Baines again had a hand, his crossfield pass headed into the area by Bilyaletdinov and Cahill superbly guiding the half-volley over the onrushing keeper's head and into the goal.
BATE briefly responded and Vitali Rodionov caused minor palpitations in the Everton ranks when he poked narrowly wide from inside the box late on, while an Igor Stasevich effort was deflected past the post with the seconds ticking down.
But, as for most of the night, Everton's defence held firm and saw out a precious win that puts them firmly in the box seat to reach the knockout stages.