Everton once again produced a Europa League performance in contrast to their domestic displays as Romelu Lukaku's late penalty secured them a 2-1 come-from-behind victory in their last-16 first leg against Dynamo Kiev.
The Toffees started the contest at Goodison Park poorly and fell behind in the 14th minute to an Oleg Gusev finish, but they improved markedly as the first half went on and equalised in the 39th as Lukaku's strength allowed him to set up a Steven Naismith strike.
Roberto Martinez's side did their best to sustain the momentum after the break, but it looked as if they would be frustrated in their attempts to add another goal.
However, a handball from Danilo Silva eight minutes from time saw referee Carlos Velasco Carballo award a spot-kick which Lukaku converted, making him Everton's all-time record European scorer with seven goals and sealing the advantage in the tie for his side.
Martinez's men have been struggling in the Barclays Premier League this term but they continue to impress in continental action and will fancy their chances of emerging from next week's second leg in Kiev with a quarter-final place booked.
They are the only British club left in the competition, and 24 hours after Chelsea's dramatic exit from the Champions League, this result also lifted some of the gloom that has been surrounding the overall performance of Premier League and Scottish Premiership sides in Europe this term.
At first, Everton seemed afflicted by the same uncertainty they have shown domestically as they came under early pressure from a dynamic Dynamo outfit.
That pressure soon reaped dividends for the Ukrainian league leaders when Antolin Alcaraz sliced the ball behind for a corner.
Andriy Yarmolenko sent it into the box and, with the Everton defence slow to react, Gusev nipped around a clutch of blue shirts to meet the delivery with a neat volley past Tim Howard at the near post.
The hosts were initially unable to get much going at all in response, aside from Kevin Mirallas thrusting his hand into the face of Atunes to earn a booking.
Sergei Sydorchuk lashed a shot off-target and saw a low drive turned behind by Howard either side of Phil Jagielka blocking Dieumerci Mbokani's header.
A chance of sorts did present itself for Everton just after the half-hour when Dynamo goalkeeper Oleksandr Shovkovskiy came haring out of his box and made a hash of his attempted clearance, with the ball falling to Lukaku, but the striker's lob was off target.
Moments later, Alcaraz caused a scare at the other end by inadvertently playing in Mbokani, who was unable to take advantage.
However, Everton then suddenly came to life. Lukaku's free-kick skimmed the top of the bar, a corner was given and from the delivery, Jagielka's header was cleared off the line by Silva, with Alacaraz subsequently shooting narrowly over.
Within three minutes of that the game was level, Lukaku battling well to hold off several Dynamo players and tee up Naismith, who slotted home.
Another home goal appeared set to follow swiftly when Mirallas took the ball around Shovkovskiy but the winger failed to pick out fellow Belgium international Lukaku.
Everton looked to keep their foot on the pedal as the second half got under way and after an Alcaraz long-range shot was fumbled by Shovkovskiy, Naismith glanced a header wide from a corner.
Dynamo replied with Mbokani nodding onto the roof of the net and Martinez then replaced Mirallas with Arouna Kone, who swiftly saw Shovkovskiy get down to claim his header.
Further efforts were traded, with Yarmolenko shooting over and a Lukaku strike gathered by Shovkovskiy.
Everton then snatched victory on the night when substitute Leon Osman diverted the ball against the hand of Silva and the resulting penalty was slotted in -- just about -- by Lukaku.
In the dying moments Lukaku's cross was nodded goalwards by Osman and Naismith failed to connect on the stretch -- but Everton fans were happy enough at the final whistle.