The tale of the first half was compacted into a three-minute period as Nigeria scored twice sandwiched either side of a gilt-edged opening for Australia.
It was 2-0 at the interval, and the game was still a contest until the final 17 minutes before Nigeria ran riot against an Australian side looking flat after surviving the ‘group of death’.
That moment came on 22 minutes as Osimhen showed just why he is the tournament’s leading goalscorer by bursting forward with pace and power on the left, before turning his defender and sliding the ball impressively inside the far post.
Australia could have drawn level immediately with Cameron Joice seeing his shot saved, while Lucas Derrick pushed the follow-up wide as a golden opportunity was spurned.
Almost immediately Nigeria were two in front as Funsho Bambgboye went to ground in the penalty area, and Kelechi Nwakali coolly slotted home the resultant penalty.
The two goals seemed to inspire the Nigerians who took a greater hold as the half wore on creating several half-openings around the Aussie goal.
Nigeria continued their powerful performance after the break, and although Australia dominated possession for periods, it was the Africans who ended the contest with a third.
Osimhen scored twice in the space of six minutes, the second with another laser-perfect drive into the top corner.
The deflated Aussies conceded to more goals in the dying minutes as firstly substitute Edidiong Michael Essien, and then Samuel Chukwueze, inflicted further pain as Nigeria stormed into the last-eight in confident fashion.