Nigeria kicked off with intent, as Osimhen had a close-range effort disallowed for offside in just the second minute.
The Super Eagles' pressure paid off in the 20th minute when Ademola Lookman scored his third goal of the tournament, latching onto a pass from Akor Adams, shaking off a defender, and unleashing a precise finish into the top corner.
Nigeria doubled their advantage just five minutes later, with Adams again the provider. Adams drilled a low delivery across the box for Osimhen to power home past hapless Mozambique goalkeeper Ernan Siluane.
The Mambas struggled throughout the first half, confined to their own territory with little possession and posing no real threat to Stanley Nwabali in the Nigeria goal. In an attempt to spark an unlikely comeback, Mozambique made a double substitution at the break, introducing Manuel Kambala and Nanani in place of Pelembe and Diogo Calila
However, Nigeria struck almost immediately after the restart, with Lookman providing a dangerous cross that Osimhen tapped in from close range just two minutes into the second half.
The scoring was rounded off 15 minutes from time when Adams capped a superb individual display by smashing home Lookman's cross, completing a dominant 4-0 victory and sealing Nigeria's progression.