The result has left Kyiv with a 3-2 record while Estonians Kalev improved to 2-3.
Depending on next week's outcomes, Kyiv and Kalev, along with BC Triumph and Deutsche Bank Skyliners, could all finish with 3-3 marks at the end of Regular Season play.
John Linehan had one of the best performances of the his career for Kalev Cramo, making eight of nine shots from long range on his way to a game-high 32 points.
The 1.75m point guard also dished out six assists and pulled down six rebounds.
Nenad Vucinic, the New Zealand national team boss and Kalev Cramo coach, spoke to his players with his usual confidence at the end of the third quarter with his side trailing 60-58.
Just 15 seconds into the fourth quarter, Nate Fox connected from behind the arc for a 61-60 Kalev lead and Linehan followed the next time down the court with a lay-up to push the advantage to three.
They went on to score eight consecutive points and capped the spurt with a Kristjan Kangur jumper.
A Goran Jeretin three-pointer 5:40 from the end brought Kyiv back to 68-67, only for Kalev to keep their noses in front with Valmo Kriisa next to score by making two free throws.
Kyiv once again closed the gap to one when Manuchar Markoishvili scored to make it 70-69 with 4:27 to go.
Linehan answered this time with one of his threes to take the lead to 73-69.
Kalev Kramo held on for a thrilling win.
Scoonie Penn poured in 19 points for Kyiv.
Sasa Obradovic, coach of Kyiv:
"It was a very good game for Kalev, specially considering the circumstanses when both teams had some problems in the first half, especially foul problems. I also have to underline John Linehan's game, he played an extraordinary game, probably the best this season and he was also hitting difficult shots over the hands [of his opponents] and we didn't react quickly enough on that. We are still missing two players; if we had those two players I think we would have made a better rotation. Congratulations once again to Kalev but we still have pretty good chance [to qualify], we just have to beat Frankfurt. That is not going to be an easy game but hopefully we will take the win."
Nenad Vucinic, coach of Kalev Cramo:
"I would like to thank our players for their effort on beating such a team as Kyiv. ESpecially after the hole we dug ourselves in early on. We stayed positive, played hard the whole game and things happened for us. I hate singling out players but i think John [Linehan] made an excellent game tonight. He made eight of nine three pointers. The guy doesn't stop the whole game, hussling, playing defense, helping everyone. And it is very good to have a player like that in our team. It was very important win for us, we are still alive, of course we have to beat Triumph and Kyiv has to beatFrankfurt. But we believe in ourselves."