Jeremain Lens' deflected first-half opener appeared as though it would be enough for Kiev to take the advantage back to Florence next week.
However, substitute Babacar showed great athleticism to flick the ball over his head from close range in the 92nd minute to earn a deserved draw at the Olimpiyskiy National Sports Complex.
And the Senegal international was delighted to play such a vital role.
Speaking to Mediaset, he said: "It was a very important game for us, we gave everything. We played a good game.
"He [head coach Vincenzo Montella] told me that I have to continue with the right attitude and give my best. I play for the team.
"We want to go all the way and win the Europa League, we're sure success will come soon.
"We'll play the return leg and maybe go even further. We must continue to work well, it was impossible to lose to Kiev after playing so well."
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