The Reds found themselves a goal down after Daniel Udoh opened the scoring, but quickly got back in control of the game thanks to first-half goals from Kaide Gordon and Fabinho.
The Brazilian defensive midfielder doubled his tally for the day in the 90th minute but not before his compatriot, Firmino, could produce a moment of magic.
Roberto Firmino (centre) wheeled away in celebration following his excellent back-heel finish
The forward entered the pitch in substitution for Elijah Dixon-Bonner and with his first few touches of the afternoon, found the back of the net.
Firmino managed to control Ibrahima Konate’s miscued effort and with his back to goal, fired a shot with his heel past Shrewsbury’s Marko Marosi.
A clip of the goal is already doing the rounds on social media and has left Liverpool fans in awe of the superb piece of skill – with one fan claiming that it was ‘vintage Firmino’.
For Liverpool, there isn’t much to shout about from a win over the 15th-placed side in League One, but out of a heavily-rotated side Klopp will have mined some encouraging information.
Firmino managed to control Ibrahima Konate’s shot and divert it into the net using his heel
The Reds booked their place in the fourth round of the FA Cup, where they’ll face Cardiff City
Most of it will centre on their equalising goal, which was built in their academy, with the assist coming from Conor Bradley, 18, and a fine finish from Gordon, 17. Combined they are younger than James Milner; in isolation, Gordon is the second youngest scorer in Liverpool’s history.
With the Africa Cup of Nations and Covid each taking a chunk out of Liverpool’s resources, including Trent Alexander-Arnold, who was revealed to have tested positive, Klopp made seven changes to the side most recently used against Chelsea.
There were four teenagers among them, and three squad numbers in excess of 80, but with the protective presence of Virgil van Dijk, Andrew Robertson and Fabinho it was difficult to forecast any serious jeopardy in the situation.