Everton rode their luck to earn victory against Metalist Kharkiv and book their place in the Uefa Cup group stage.
Everton celebrate after McFadden's crucial goal against Metalist
Metalist dominated proceedings and took a deserved lead when Edmar played a one-two with Marko Devic and shot home.
Everton levelled when Joleon Lescott deflected in Steven Pienaar's drive, before Hicham Mahdoufi fired in after Olexandr Rykun's shot hit the post.
James McFadden rifled into the corner from 18 yards and Victor Anichebe's solo effort settled it late on.
The result was desperately harsh on the Ukraine side, who had controlled so much of the game to come out of it with no reward.
The home fans provided an electric atmosphere from the kick-off, with every Metalist attack greeted by a deafening crescendo of cheers.
Everton were struggling to get a foothold in the game and they nearly went behind early on when Edmar found himself unmarked on the edge of the box and forced a good low save from Tim Howard.
Everton's first real attack came when McFadden surged into the box and fell between two challenges, but seconds after his penalty appeal was turned down, David Moyes' men were behind.
Edmar cleverly exchanged passes with Devic and the Brazilian made no mistake with his second chance of the game, coolly slotting left-footed past Howard.
James McFadden's first-half penalty claim fell on deaf ears
The Toffees needed a reply and they so nearly got one when Pienaar whipped over a superb cross from the left, Leon Osman planting his header straight into Oleksandr Goryainov's arms from point-blank range.
The teams then traded 25-yard shots, McFadden slamming just over before Metalist's Valentyn Sliusar rifled wide at the other end.
Whatever Moyes said during the interval paid immediate dividends as his side wasted no time in getting back on level terms.
Goryainov punched away from Yakubu but Everton pumped the ball back into the box and when Pienaar's shot was deflected into Lescott's path, the defender turned in his fifth goal of the season.
If Metalist were unlucky not to still be ahead, they did not mess around feeling sorry for themselves.
They tore up the other end, Rykun's 20-yard shot cannoned off the inside of the post and Mahdoufi was on hand to belt the rebound home.
Everton were once again staring down the barrel and Moyes crucially threw Anichebe on as they pressed for another equaliser.
McFadden was sent through by Lescott only for Goryainov to save well at his feet, before the lively Pienaar wasted two good openings.
With 18 minutes left, McFadden finally broke the Ukraine team's hearts, collecting Anichebe's pass and firing past Goryainov from 18 yards.
It was the 19-year-old Anichebe who wrapped it up with two minutes left, taking advantage of a poor defensive header, keeping his composure and hammering into the net.
Suddenly, it was the silence from the 27,500 crowd that was deafening.
Everton boss David Moyes:
"I just want to have a run in Europe.
"I'm delighted for the players and myself as this is something I really want to do. Metalist proved once again that they are a very good team tonight.
"They made it hard for us and we are just delighted to have got through."
FC Metalist Kharkiv : Goryainov, Bordiyan (Nwoha 85), Mdrakovic, Guie, Mahdoufi, Valiaev, Edmar, Rykun, Devic (Zeze 90), Jakobia (Danilav 74), Slysur.
Subs Not Used: Thumak, Davydov, Svitlychny, Kostyuk.
Goals: Edmar 21, Mahdoufi 52.
Everton: Howard, Neville, Yobo, Stubbs, Lescott, Pienaar, Jagielka (Anichebe 62), Osman, Arteta, McFadden (Hibbert 90), Yakubu (Baines 76).
Subs Not Used: Wessels, Nuno Valente, Carsley, Jutkiewicz.
Booked: Neville, Baines.
Goals: Lescott 48, McFadden 72, Anichebe 88.
Ref: Jouni Hyytia (Finland).