Romelu Lukaku’s late penalty gave Everton a vital lead to take to Dynamo Kiev after the first leg of their Europa League last-16 tie.
A bad week for English clubs in Europe seemed to be getting worse when Oleg Gusev swept the Ukrainian side ahead.
The home side had started slowly but Lukaku’s brilliant run teed Steven Naismith up to level before the break.
And the striker converted from the spot after Danilo Silva handled in the area to give the Blues a slender lead.
If they can hold it in Ukraine on 19 March, Everton will set up a first European quarter-final in 30 years, an achievement set against the backdrop of a woeful league campaign.
Manager Roberto Martinez has conceded his side, six points above the relegation zone, face the harsh reality of a scrap for league survival but European commitments continue to offer respite.
Lukaku, much maligned for his league form in recent weeks, became the club’s record European goalscorer with seven goals when his penalty squirmed under 40-year-old goalkeeper Oleksandr Shovkovskiy with eight minutes remaining.
The Belgian impressed throughout, completing 86% of his passes and the visitors, who have never won in England, were often stretched by his runs into channels.