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.