Liverpool overcame Tranmere Rovers 3-2 at Prenton Park in a friendly on Tuesday, but their win was overshadowed by another error from goalkeeper Loris Karius.
The visitors opted to field two completely different teams in each period, as they also did in their win at Chester on Saturday, with their first-half line-up giving Jurgen Klopp's side a 3-0 lead at the break.
Liverpool made the breakthrough after fine approach play down the right from Sheyi Ojo, with the exciting winger then setting up Portugal midfielder Rafael Camacho for a simple finish.
Liverpool doubled their lead after 27 minutes when Naby Keita, playing alongside fellow new signing Fabinho in central midfield for the first time, found Ojo in space.
The England U21 international then got past his marker, before firing a left-footed shot into the bottom right-hand corner of the net.
Two soon became three when Ryan Kent's brilliant flick released captain Adam Lallana in the area and the midfielder's early strike caught the Tranmere 'keeper off guard.
However, after Liverpool made a raft of changes at the interval, the home side got themselves back into the contest, albeit after another Karius mistake.
The German, whose high-profile errors cost Liverpool in last season's Champions League final against Real Madrid, failed to hold on to Ollie Norburn's long-range free kick, with Jonny Smith scoring from the rebound.
Despite adding a second nine minutes from the end through Amadou Soukouna, Liverpool held on to make it two pre-season wins from two ahead of their trip to Bury on Saturday.