Lucas Leiva scored his first goal in almost 7 years to put the reds into the next round of the FA Cup.
The reds picked a stronger attacking line up than the first leg at Anfield that ended 0-0, but it was still LFC's second youngest ever starting XI.
Lucas captained the side, but Daniel Sturridge also returned to the starting line up. Coutinho made his first start since injury - his last two appearances being off the bench.
Paulo Alves and Harry Wilson were named and in the second half Wilson came on for his LFC debut.
From the outset Plymouth showed more determination than they had in the first leg and they had themselves a corner within the first minutes of the game.
But they were defensively resolute too - frustrating the reds at times.
The Liverpool goal arrived in the 18th minute, when 30 year old Lucas met Coutinho's corner with his head at the near post. His header went in at the near post and the reds were 1-0 up.
— BT Sport Football (@btsportfootball) 18 January 2017
There was little other excitement in the half although just minutes after our goal - Loris Karius was called into action to beat away a Plymouth effort.
The home team didn't lose their desire and in the second half, particularly after the reds took Coutinho off, they tested Karius with some crosses and set pieces. The League Two side appeared to favour attacking Moreno's wing as opposed to Trent Alexander Arnold who displayed some excellent positioning.
With 15 minutes to go Plymouth had a great chance to equalise, Jervis finding himself unmarked in the middle of the box but his hooked shot went just away from the goal.
Klopp hauled Daniel Sturridge off who had a poor night and couldn't break through Plymouth's rearguard - bringing on Sheyi Ojo.
Divock Origi wasn't doing any better than the England striker however, and when Moreno was fouled in the area with 5 minutes left - the Belgian striker stepped up to take the penalty.
He is no James Milner though and his penalty was saved. Moments later he had a chance to redeem himself but he shot over the bar from the edge of the area.
Liverpool, not at their best, to quote a sporting phrase they 'won ugly'.
The reds will meet Wolves at Anfield in the 4th Round. Next up is a visit by Swansea to Anfield in this weekend's Premier League.
Lucas: 'Has it been that long since I scored? I scored last week in training.'
— Anfield Online (@anfieldonline) 18 January 2017