Ireland's hopes of winning the Nations League B group already look forlorn ahead of Scotland's visit to Dublin on Saturday following successive defeats by Armenia and Ukraine.
Vitaliy Mykolenko drilled an early attempt wide as playmaker Mykola Shaparenko started to make his influence felt.
As the tempo settled, so too did Ukraine and Shane Duffy had to throw himself into the path of Serhiy Sydorchuk's drive before Caoimhin Kelleher dealt ably with Oleksandr Zubkov's well-struck effort.
Ireland were spared with eight minutes of the half remaining when Taras Kacharaba's strike was ruled out for offside during the build-up following a VAR review.
Ukraine took the lead when Tsygankov's in-swinging free-kick eluded everyone in the middle and flew inside Kelleher's far post.
The hosts almost snatched a 79th minute equaliser when Duffy powered his header against the bar.
DUBLIN (AFP) - Viktor Tsygankov lifted Ukraine's spirits after their painful failure to qualify for the World Cup as the midfielder clinched a 1-0 Nations League victory over the Republic of Ireland on Wednesday (June 8).
Tsygankov struck with a fine free-kick early in the second half at Dublin's Aviva Stadium.
Ukraine held on to that slender lead as they bounced back from the 1-0 defeat against Wales on Sunday that ended the war-torn nation's bid to qualify for this year's World Cup.
While Ukraine won't be going to Qatar for the World Cup, their impressive response to such a devastating loss epitomised the spirit in Oleksandr Petrakov's side.
Of course, Petrakov's players have far greater concerns as the Russian invasion continues in their homeland.
The Irish FA had handed out 3,500 tickets to Ukrainian refugees and there were other pockets of blue and yellow around the Aviva Stadium.
"This is a very difficult time. The Ukrainians who came to see us play in Ireland were accepted by the incredible Irish hospitality and people," Petrakov said.
"You took our women and children who were basically risking their lives back in Ukraine. I want to thank the whole island.
"Those Ukrainians in the stand just wanted to see some positivity from the team but they are really longing to go home to Ukraine.
"We made them a little bit happier tonight. That is the major achievement in my view."
Petrakov had admitted the emotional and physical impact of the events in Cardiff combined with the ongoing war had taken its toll on his players.
He made 10 changes after the Wales game and the understudies were good enough to extend Ireland's winless run in the Nations League to 12 games.
"Overall, I'm happy with the result and with the attitude and performance. It is a very positive thing for the team especially after such a bitter result in Wales. We turn the page and we look forward to our future," Petrakov said.