The Enugu-based club drew 1-1 with the Beninese side in Friday’s second leg at Stade de Kegue in Lome, with the result leaving the tie level at 2-2 on aggregate.
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Rangers took the lead in the 22nd minute when Sobemap conceded an own goal, but the hosts responded to equalise with 25 minutes remaining.
Neither side could find a decisive goal during regulation time, sending the tie into a penalty shootout.
The Nigerian side kept their composure to win 5-4 from the spot and book their place in the next round.
Following this result, Fidelis Ilechukwu’s side will face Algerian giants MC Alger.