Wykeen Kelly's match-winning shot saw Khimik get their EuroCup Group D campaign off to a perfect start on Wednesday.
The guard made a three-point shot to snatch a late victory at home against Cholet Basket - sending the Ukrainian side to a 75-72 result.
Nando De Colo could have drawn his side level right at the death but he missed a shot from behind the arc with just three seconds of play left.
Sasa Bratic top-scored for the hosts with 23 points while Edward Richard Basden sunk 18 for Cholet.
The French side were quick out of the blocks, pouring in six points with no reply in just over two minutes.
But, despite trailing Cholet by eight points at one stage, Khimik clawed their way back into the game to finish the quarter 19-16 behind.
Anthony Dobbins poured in eight points in the second period to lead 39-28 at the halfway stage of the game, before the Ukrainians responded again to go into the final ten minutes just one point behind their opponents.
Khimik took the lead for the first time nine seconds into the final quarter to set off a nervy tense period with both sides tussling for the advantage.
But Kelly's shot with 14 seconds left on the clock proved decisive.
The Ukrainians join next opponents Barons LMT at the top of the group.