Taiwo Maiyegun and Chris Akpogua scored in both halves for the lower division side as they claimed a famous win to make their first ever Cup semi-final.
Enyimba, stunned by the score, left it late to haul themselves back into the game, but Prime held firm to spark celebrations at the end.
Compared to Enyimba, Kano Pillars had a more straightforward, if equally challenging test to overcome Plateau United in Lagos.
Pillars triumphed 3-2 in the end, but will consider themselves fortunate. The northern aristocrats had to rally from going behind early to book their last four spot.
In other games, Lobi Stars topped Sharks 3-1, as the Port Harcourt club's long wait for a trophy continues.
Heartland also made it past Crown, claiming a 2-0 victory to make the semi-final.