Matteo Boniciolli's Italians, who needed to win to guarantee a place in the Quarter-Finals, prevailed 69-57.
The result knocked EWE Baskets Oldenburg out of contention for a last-eight place.
EWE Baskets had needed to win at Galatasaray on Tuesday and for Virtus, whom they beat twice, to lose in order to advance.
Reshawn Terry had 16 points for Virtus, with Finland international Petteri Koponen and playmaker Earl Boykins contributing 15 apiece.
Kyiv are still in the last eight.
They won their fourth game in the group last week to seal their progression but ended up second in the pool after losing both of their games to Virtus.
Kyiv only trailed 49-43 after Manuchar Markoishvili made a lay-up for the first two points of the fourth quarter.
Ntousan Tsalikis-Vouktsevits replied with a three-ball to settle the Virtus nerves.
After Oleg Saltovets split a pair of free throws for Kyiv, the Italians answered with a 9-0 run.
Six of the points were scored by Terry.
He made a jump shot, then a lay-up and after Boykins sank a three, Terry dunked.
The lead ballooned to 67-47 on a Keith Langford three-ball just 2:39 from the end before Boniciolli's men finished with a 12-point triumph.
Artur Drozdov led all scorers with 20 points for Kyiv.
"I have to congratulate Kyiv. After they dismissed their players people must have thought they gave up their hopes of advancing. But the way they played and the way they are coached they certainly deserved to advance. I hope we face each other again in the Final Four. I also want to thank my players - this was our eighth game during the last 19 days, they still fought throughout the contest. Special thanks to Earl Boykins, who led the team."
Sasa Obradovic, coach of BC Kyiv:
"First thing I told my players in the dressing room is that I am not upset with the loss. I think we deserved to go through because of the way we played in the last few weeks. But this game also showed the difference in levels. Virtus with their hopes of winning a top European league and us, who with young players have a long way to go before we achieve something."
Artur Drozdov, player BC Kyiv:
"We are not ashamed, no way. We advanced and that's what matters. We'll be ready for Cholet basket now."