Quick-fire goals from Oleksandr Zinchenko and Roman Yaremchuk cancelled out first-half efforts from Joe Aribo and Victor Osimhen in Dnipro.
It did not take long for the Super Eagles to establish their dominance at the Dnipro Arena with an early goal from debutant Aribo.
Samuel Kalu dazzled the Ukraine defence with his piece of skills before singling out Alex Iwobi who assisted the Rangers midfielder to break the deadlock in the third minute.
Samuel Chukwueze came close to double the lead for the visitors but goalkeeper Andriy Lunin was on alert to save the Villarreal star's effort.
Despite the absence of key players like captain Ahmed Musa, Gernot Rohr's men were dominant in the opening minutes of the game and kept Ukraine on their toes.
Aside from the constant attacking threats from Nigeria, Francis Uzoho turned up to the party in Dnipro as well to deny Andriy Shevchenko's team a goal in the first half.
Three minutes after the hour-mark, the Super Eagles doubled their lead with red-hot Lille star Osimhen scoring his maiden goal for the senior national team.
Kalu was tripped by Eduard Sobol in the penalty area and Osimhen stepped forward to convert the resulting kick.
Shortly after conceding a second goal, Ukraine were dealt an injury blow as Shakhtar Donetsk forward Junior Moraes was replaced by Yaremchuk.
Nigeria continued their dominant display in the second 45 minutes but Ukraine came close to cutting the deficit in the 62nd minute but Uzoho did well to stop a free-kick from second-half substitute Marloes.
In the last 20 minutes of the encounter, Rohr threw PAOK midfielder Anderson Esiti and Moses Simon into the fray for Iwobi and Kalu respectively.
Ukraine finally broke the Super Eagles resistance in the 78th minute, thanks to Zinchenko's brilliant movement and finish.
A minute later, Yaremchuk found the back of the net to draw the hosts level as both teams settled for the spoils in Dnipro.
Meanwhile, William Troost-Ekong picked up an injury in the closing stage of the encounter and had to be replaced by Leganes' Chidozie Awaziem.