Ukraine trailed inside five minutes as Valencia's Lee Kang-in converted from the penalty spot, but Supriaha found the net either side of half-time and Heorhii Tsitaishvili rounded off the scoring late on.
Saturday's final in Lodz featured two first-time finalists and it was South Korea who made the brighter start thanks to Lee's spot-kick, awarded after VAR ruled Kim Se-yun had been fouled just inside the area.
Supriaha profited from some slack defending to tap in an equaliser in the 34th minute, however, and he added Ukraine's second shortly after the break after being inadvertently played in by Korea's Kim Hyun-woo.
Ukraine then had Real Madrid goalkeeper Andriy Lunin to thank for keeping them in front when he pushed Lee Jae-ik's header on to the frame of the goal.
Lunin, who spent last season on loan at Leganes, not only picked up a winners' medal, but also earned himself the Golden Glove accolade, after keeping clean sheets in the 1-0 wins over Qatar in the group stages and Italy in the semi-finals.
Red Bull Salzburg striker Erling Haland won the Golden Boot, netting a whopping nine goals for Norway at the tournament despite not getting out of the groups.
His tally was five ahead of his nearest competitors, and all his goals were scored in one game - a 12-0 demolition of 10-man Honduras.
Meanwhile, Lee Kang-in was awarded the Golden Ball, a small consolation for defeat in the final.
Japan, who were eliminated by Lee Kang-in's side in the quarter-finals, picked up the Fair Play Trophy.