Debuts were handed to Aly Cissokho and Luis Alberto as a strong Liverpool side hoped for a safe passage to the third round and they made the perfect start as Sterling scored in the fourth minute after powering down the middle and drilling a shot past the diving Bialkowski to send Anfield wild.
However, there was bad news in the 10th minute as Cissokho went down injured and had to be replaced by Agger ruining his debut but Agger nearly made an instant impact as he met Gerrard's free-kick to glance a header at goal which cannoned off the post.
Sturridge continued his run of scoring in successive games as he collected a pass from Gerrard and rifled a shot into the far corner for a 2-0 lead, Agger came close to adding a third when he nodded towards goal but found the palms of Bialkowski.
As half-time approached, Gerrard continued the Liverpool threat as he latched on to a pass from Sterling and smashed a shot against the near post which meant Liverpool lead 2-0 at the break. Early in the second half, it was clear that Liverpool's approach was more reserved and County had a chance through McGregor but from 30 yards out he failed to test Mignolet who saved with ease.
County used that chance to spur them on and it bore fruit minutes later as they reduced the deficit from a clever free-kick, Smith glanced a header across goal allowing the onrushing Arquin to nod past Mignolet from six yards.
Liverpool were thwarted by the post again when Toure met a Gerrard cross on the volley which beat Bialkowski but didn't find the net but with six minutes remaining, Liverpool came unstuck as Arquin surged through the defence and swept in a cross which was met by substitute Coombes who tucked the ball past Mignolet to level the tie and send the away fans into ecstasy.
The prospect of extra-time loomed as Agger took a go from 25 yards that took a delfection and flew off target and Sterling sliced Johnson's cross past the post. Extra-time began and Liverpool were dealt another defensive blow as Toure went off injured leaving them with 10 men having used all three substitutes.
Despite the numerical disadvantage, Liverpool regained the lead as Sturridge finished off a rapid counter-attack which saw Coutinho find the striker in open space and pick him out to allow him to drill a shot from a tight angle that got a touch from Bialkowski but not strong enough to prevent Liverpool leading 3-2.
A safe passage to the third round was endured after a pacy run by Jordan Henderson saw him nutmeg Liddle before sweeping the ball past Bialkowski to seal a 4-2 win. Liverpool made it hard as has become a tradition against lower-league sides in the cup so maybe a tie against a fellow top-flight team in the next round may see them keep their foot on the gas rather than backing off in the second half.