Jurgen Klopp's side taken off into the Birkenhead sun wearing their new purple away pack, with the administrator handling another improvised side as Adam Lallana wore the commander's armband.
It took only seven-and-a-half minutes for the guests to break the gridlock, with Sheyi Ojo's diligence down the correct flank permitting Rafa Camacho to slice inside and fire home to make it 1-0.
Ojo added to the scoresheet himself just before the half-hour, getting the ball on the wing, toying with Mark Ellis and driving low past goalkeeper Scott Davies from a tight point.
The Reds' third came following a scramble in the punishment zone, with the amazing Andy Robertson in the end backheeling towards Lallana who put his foot through it and into the back of the net.
Ryan Kent and Dominic Solanke joined for a late open door that was spurned by a fine handle, in what could turn out to be a fitting depiction of the twosome's prospects.
Klopp rolled out 11 improvements at the break, with Harry Wilson taking up his situation on the privilege of a 4-2-2-2 on the back of marking another five-year contract with the Reds.
Loris Karius was given an essence of things to come when a standard catch was met with unexpected cheers, and the effect was pounded home promptly as he shanked his endeavored pass.
Following Solanke's lead from the primary half, Divock Origi kept on battling before objective, impacting an exertion high and wide in the wake of being encouraged through on the right-hand side of the case.
Also, Liverpool yielded before long, with Karius spilling a free-kick from Ollie Norburn, enabling Jonny Smith to development and diminish the deficiency in a remorseless blow for the No. 1.
Karius was less to blame for Tranmere's second, with Pedro Chirivella's poor back-pass permitting Amadou Soukouna through to make it 3-2.
Having been condemning of his side's show in the principal half at Chester, Klopp will have been baffled after half-time at Prenton Park, as his adjusted side neglected to discover any cadence.