A last-gasp header from substitute Claudio Beauvue gave Celta Vigo a slender 2-1 lead over Krasnodar after the first leg of their Europa League last-16 tie.
Celta looked set to be heading to Russia for the return match at a slight disadvantage, but substitute Beauvue's 90th-minute effort gave them the upper hand.
Daniel Wass' had put Celta ahead with a tremendous 35-yard free-kick early in the second half, but Viktor Claesson responded with an equaliser six minutes later.
But the late winner from Beauvue – who only replaced John Guidetti with 12 minutes remaining – clinched the victory for Celta and restored some confidence following a 5-0 thumping from Barcelona last week.
This is already the furthest Krasnodar have ever progressed in a European competition after overcoming Fenerbache in the last round, but Igor Shalimov's side still remain comfortably within reach of a quarter-final berth due to their away goal.
Celta now face the gruelling 3,800-kilometre trip for next Thursday's match, when they will look to reach the last eight of a European competition for the first time since 2001.
In a cagey opening, the home side particularly struggled for fluency. However, it was a flowing Celta move that woke the game from its slumber in the 20th minute, when Iago Aspas, Pione Sisto and Hugo Mallo combined during a breakaway to tee up Guidetti, whose header was too close to Krasnodar goalkeeper Stanislav Kritsyuk.
A flurry of Celta chances followed as they began to take control. First Kritsyuk beat away a swerving Marcelo Diaz strike after 25 minutes, before Guidetti swept a pinpoint Mallo cross inches wide and then headed over.
Krasnodar's best opening of the first half fell via a knockdown to Claesson on the edge of the box, but the winger slipped at the vital moment as he prepared to shoot.
It took a moment of individual brilliance for Celta to break the deadlock shortly after the interval. Wass' stunning free-kick dipped and bounced awkwardly in front of Kritsyuk and cannoned in off the left post.
That opener spurred the previously docile Krasnodar into action, and Vyacheslav Podberezkin rifled their first shot on goal just over from the edge of the box.
The visitors had their equaliser in the 56th minute thanks to a clever piece of footwork in the box from Claessen that dumbfounded two Celta defenders and left him with a clear run on goal to poke underneath the onrushing Sergio Alvarez.
A lovely one-two between Cristian Ramirez and Claesson almost completed a shock turnaround, but the former's shot was blocked by Alvarez.
And just as the match appeared to be heading towards a draw, Celta struck in the final minute of normal time.
Mallo found space on the right and swung in a lovely cross for Beauvue to head into the top-left corner, past the sprawling Kritsyuk for a 2-1 advantage going into next week's crucial second leg.
