First-half goals from Rafael Camacho, Sheyi Ojo and Adam Lallana ensured the Reds went in at half-time with a lead that fairly reflected their control of proceedings at Prenton Park.
And, after Jürgen Klopp had again made 11 substitutions at the break, the Reds bossed the early stages of the second half, too, until a late flurry from Tranmere brought the home team goals from Jonny Smith and Amadou Soukouna.
The visitors - wearing their new 2018-19 away kit for the first time - could have increased their advantage after those strikes, with Daniel Sturridge twice being denied by fine saves, but it finished 3-2.