Ireland had the opening chance of the game after seven minutes, Conor Tuite however was unable to connect with Ryan Nolan’s pull back from the edge of the area, a let off for Ukraine.
The number one seed’s at Rio 2016 then showed their class and came close on four separate occasions over the next four minutes before taking the lead after 12 minutes.
Ireland worked to clear a corner before Vitaliy Trushev found Vitali Romanchuk at the by-line who calmly curled the ball past Aaron Tier.
Ukraine captain Volodymyr Antoniuk made it 2-0 three minutes later finding the Irish top corner, collecting Romanchuk pass after an excellent dummy from Krasylnykov.
Antoniuk doubled his total for the day on 17 minutes, again finding the top corner after Molodstov ball had split the Irish defence.
Ukraine continued to dominate the first half and made it a four goal cushion four minutes before half time, Molodstov blasting home from the edge of the box after some last ditch Irish defending.
The tournament favourites picked up where they left off in the second half with Molodstov finding the top corner from the edge of the box for his second goal of the game.
Artem Krasylnkov curled home a free kick from the edge of the box on 38 minutes to make it 6-0. Substitute Dillion Sheridan made Ukraine keeper Smashko work with an edge of the box drive moments later.
Sheridan came close again to getting on the scoresheet with eight minutes remaining flicking on Luke Evans ball into the box, Ukraine keeper Symashko was equal to the effort.
Ireland’s second game in Group A is against host country Brazil on Saturday, kick off 11pm Irish time. Brazil had defeated Great Britain 2-1 in the group’s first game.
Ukraine: Symashko, Trushev, Dutko, Romanchuk (Shkvarlo 54), Molodtsov (Zinoviev 43), Antoniuk (Podolskyi 43), Krasylnykov
Substitutes: Len, Kahramanian, Dotsenko, Kulynych
Ireland: Tier, McKee, Evans, Markey, Tuite (Birt 38), Messett, Nolan (Sheridan 38)
Substitutes: McGillivary, O’Flaherty, Walker, Badun, Cotter
Referee: Alexandra Santos (Brazil)