Rovers drew 1-1 with Posh last Saturday and will now host their higher league opponents at Prenton Park next Wednesday evening, with a 7.45pm kick-off in front of the BT Sport cameras.
Substitute Andy Cook forced Tranmere a replay after Jack Marriott put Peterborough in front.
The winners will be away at either Woking or Bury in the second round.
BT Sport have also selected to televise Billericay Town's replay with Leatherhead next Thursday.
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