Second-half goals from Takumi Minamino and Divock Origi sent Jurgen Klopp's men into the quarter finals but North End pushed them all the way.
They could quite easily have got control of the tie had they taken some great chances in a first half when they were the more threatening team.
Brad Potts saw a shot tipped over the bar when clear on goal before a triple chance should have resulted in PNE going in front.
Sean Maguire was denied at close quarters by Reds goalkeeper Adrian, with Ryan Ledson's follow-up blocked on the line by Neco Williams before Potts blazed the third bite of the cherry too high.
Minamino broke the deadlock just beyond the hour mark, with Origi producing a cheeky flicked finish over his shoulder for the second with five minutes left.
The performance was much improved on the tame show at Blackpool at the weekend
North End's starting XI had shown nine changes from the side which had played at Bloomfield Road, Sepp van den Berg and Andrew Hughes the two to keep their places.
The 3-5-2 system remained, van den Berg, Liam Lindsay and Hughes the three at the back, with Joe Rafferty and skipper Greg Cunningham in the wing-back roles.
Ali McCann returned from a three-week absence with an ankle injury to link-up with Ryan Ledson and Brad Potts in midfield.
Up front, Tom Barkhuizen partnered Maguire, this Barkhuizen's 200th appearance for PNE.
Liverpool had all the possession early doors without threatening with any chances, North End building into the game and growing in confidence.
They should have gone in at half-time ahead, having carved out some good chances as the first half went on.
Barkhuizen fired over the bar from 20 yards after chasing a pass through the Liverpool half and getting across his marker, while Ledson hooked a volley too high from the edge of the box.
In the 25th minute, Maguire's through ball sent Potts racing clear on goal, the midfielder reaching the edge of the box before shooting, Adrian reaching up to tip the effort over the bar.
Their best chance of breaking the deadlock came three minutes after that chance for Potts.
McCann got down the right hand side of the box and pulled a low cross into the middle which found Maguire seven yards out,.
His first-time shot was saved at point-blank range by Adrian, the rebound falling to Ledson who drove a shot goalwards where it struck Neco Williams covering on the line.
The ball bounced off his chest into the path of Potts who blazed the third shot of the sequence over the bar.
Just after the half-hour mark, van den Berg blocked a shot from Alex Oxlade-Chamberlain.
Liverpool brought off Joel Matip at the interval and replaced him at the back with Nat Phillips.
A couple of long throw-ins from Barkhuizen forced the visitors into clearances deep in their box in the early stages if the second half.
At the other end, Oxlade-Chamberlain had a shot from the edge of the box which bounced just wide of the target.
Rafferty's cross from the right-wing found Barkhuizen on the far side of the box on the hour, his side-foot volley lacking power and gathered by Adrian at his near post.
Within a minute, Liverpool attacked at the other end and scored with their first effort on target.
Williams got down the right side of the box and crossed low to the near post where Minamino steered it across Declan Rudd.
North End made their first substitution just after the goal, Emil Riis replacing Barkhuizen who had looked strong and full of running up front.
Josh Earl then replaced Cunningham at left wing-back, before a triple sub came in the 77th minute - Daniel Johnson, Ben Whiteman and Scott Sinclair joining the action in place of McCann, Ledson and Maguire.
In the 80th minute, Curtis Jones fired a low shot from the edge of the box straight at Rudd who gathered comfortably.
Liverpool scored their second goal in the 85th minute, Kostas Tsimikas' cross from the left deceiving Rudd and bouncing against the bar.
The ball dropped to Williams on the corner of the six-yard box who knocked the ball into the middle, Origi flicking a shot over his shoulder and into the net.
In the 90th minute, Williams got clear on goal but Rudd dashed off his line to spread himself and block superbly.
PNE: Rudd, van den Berg, Lindsay, Hughes, Rafferty, Ledson (Whiteman 77), McCann (Johnson 77), Potts, Cunningham (Earl 68), Maguire (Sinclair 77), Barkhuizen (Riis 63). Subs (not used): Bauer, Storey, Huntington, Iversen.
Liverpool: Adrian, Williams, Gomez, Matip (Phillips 46), Tsimikas, Morton, Oxlade-Chamberlain (Dixon-Bonner 90), Jones (Beck 90), Blair (Bradley 55), Minamino, Origi. Subs (not used): Konate, Firmino, Jota, Hughes, Pitaluga.
Referee: David Coote (Nottinghamshire)
Attendance: 22,131 (5,611 away)
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