Reds goalkeeper Caoimhin Kelleher, who starred throughout this competition last season, was the hero once again as he saved three of Derby's five penalties to help his team edge through to the fourth round after a dramatic shoot-out.
Liverpool made 11 changes from the starting XI which defeated Tottenham Hotspur 2-1 in the Premier League on Sunday, with the only players in their side to have started a league game this season being defenders Joe Gomez, Kostas Tsimikas and Nathaniel Phillips, as well as attacking midfielder Fabio Carvalho.
The majority of Anfield thought their side had taken the lead early in the first half when Alex Oxlade-Chamberlain's effort from the edge of the area marginally went wide before striking a steward behind the goal and deceiving the crowd by hitting the back of the net.
Debutant Layton Stewart should have opened the scoring moments before half-time after pouncing on a loose touch from Derby defender Eiran Cashin, but the teenager blazed over from Carvalho's clever return pass.
Stewart almost made amends after the break with his deflected effort almost catching out the opposition goalkeeper Joe Wildsmith, with Derby wasting a precious moment in transition after the hosts were left short-staffed in defence.
Liverpool's cavalry arrived in the 65th minute in the form of substitutes Darwin Nunez, Harvey Elliott and Roberto Firmino, with the latter two players almost immediately linking up to great effect, but Firmino was denied at close range.
However, that was the closest either side came with Paul Warne's side superbly keeping their illustrious opponents at bay, before referee Tony Harrington blew his whistle for full-time to instigate a penalty shoot-out.
After David McGoldrick coolly blazed his penalty into the roof of the net, Jurgen Klopp's side appeared to be in a spot of bother when Wildsmith illegally rushed off his line to deny Stefan Bajcetic, with no VAR available to force a re-take.
However, Conor Hourihane was denied by Kelleher before Oxlade-Chamberlain blasted Liverpool level in off the post, with Kelleher diving to his opposite side to superbly stop Craig Forsyth's penalty.
Firmino - who was left out of Brazil's World Cup squad earlier this week - squandered the opportunity to move the Reds ahead for the first time on the night by blazing over the bar, before Louie Sibley and Nunez both dispatched to set up a sudden death scenario.
Incredibly, Republic of Ireland stopper Kelleher still had room for one more heroic save to deny Everton loanee Lewis Dobbin, with Elliott converting the winning penalty to ensure that his side's trophy defence lives on for another round at least.