It was one of those nights that reminded us why the FA Cup third round is so special, even if Liverpool ended up surviving the sort of giant-killing that would have troubled Jürgen Klopp for years to come. Plymouth Argyle, 67 places below Liverpool on the league ladder, played with courage and spirit throughout and came within the width of an upright of taking this replay into extra time.

FA Cup fourth round draw • Blackburn Rovers v Blackpool • Burnley v Bristol City • Chelsea v Brentford • Crystal Palace v Manchester City • Derby County v Leicester City • Fulham v Hull City • Lincoln City v Brighton & Hove Albion • Liverpool v Wolves • Manchester United v Wigan Athletic • Middlesbrough v Accrington Stanley • Millwall v Watford • Southampton v Arsenal • Oxford United v Newcastle United • Rochdale v Huddersfield Town • Sutton United v Leeds United • Tottenham Hotspur v Wycombe Wanderers Ties to be played 27-29 January

Instead the Premier League club prevailed and can look forward to a fourth-round tie at home against Wolverhampton Wanderers on Saturday week courtesy of a collector’s item from Lucas Leiva. Now in the twilight of his Liverpool career, the 30-year-old chose an opportune moment to rediscover his touch in the opposing box with an 18th-minute header – his first competitive goal since September 2010.

Plymouth could have been forgiven for fearing the worst at that point but, to their immense credit, the League Two side responded superbly and pushed Liverpool right to the end, coming agonisingly close to an equaliser in the closing stages when Jake Jervis met Sonny Bradley’s knock-down with a wonderful scissor-kick that clipped the post.

For Jervis, and Plymouth, it was a case of what might have been on a night when more than 17,000 crammed into Home Park, the majority of them hoping to see a little bit of history created. They never got their wish but Derek Adams, the Argyle manager, and his players are entitled to take great encouragement from the fact that Liverpool were only able to score once against them over the course of 180 minutes.

It would have been twice had Divock Origi dispatched a late penalty but the Belgian telegraphed his intentions and Luke McCormick saved it. It was a moment that rather summed up Origi’s night. Daniel Sturridge, who was substituted in the second half, was another Liverpool player who made little impression.

For Klopp, who named a stronger side than the one that was held by Plymouth at Anfield yet still included four teenagers from the start, relief must have been the overriding emotion at the end. This was an awkward occasion in every respect, right down to the moment when one of the locals presented him with a giant pasty in the post-match press conference. Klopp smiled for the cameras before politely making the point that he would let someone else eat it on the way home.

Among the few positives on the pitch for Klopp was the sight of Philippe Coutinho coming through 65 minutes unscathed. It was Coutinho’s first start of any description since he damaged ankle ligaments against Sunderland in November and by the time he made way for Harry Wilson, the 19-year-old Welshman who was making his Liverpool debut, the Brazilian had left his mark on the game.

That Coutinho was involved in Liverpool’s opening goal was no surprise. The same, however, cannot be said for the identity of the scorer. To put Lucas’s goal drought into context, Roy Hodgson was in charge at Anfield when he last scored for the club. This time the pleasure was all Klopp’s as Lucas got away from Paul-Arnold Garita to meet Coutinho’s corner with a near-post header that McCormick got a hand to but was unable to keep out.

The goal did nothing to discourage Plymouth’s players or their vociferous supporters as the home team played with far more ambition than they showed in the 0-0 draw at Anfield. They produced some nice passages of play, especially in the first half, when the only thing missing was a goal.

The hosts came close on a couple of occasions. Oscar Threlkeld scampered forward from right-back, skipped past one challenge and delivered a dangerous low centre that Garita seemed destined to turn home, only for Trent Alexander-Arnold to make a superbly timed interception. Graham Carey had earlier tested Loris Karius from distance, forcing the Liverpool goalkeeper Loris Karius to claw the ball away from distance.

Plymouth Argyle v Liverpool: FA Cup third round replay – live! Read more

The pattern of the game remained the same in the second half as Plymouth, working tirelessly, continued to make life difficult for Liverpool, who enjoyed more possession but never looked particularly threatening. Sturridge, running on to a pass from Lucas, ought to have done better with a close-range volley.

Then came Jervis’s chance as he swivelled to spectacularly sweep Bradley’s header past Karius and on to the outside of the post. It was a reprieve for Liverpool and one that they should have punished in the closing minutes, when Yann Songo’o brought down Alberto Moreno in the area. Graham Scott, the referee, pointed to the spot but Origi was unable to convert.

Plymouth sensed it could still be their night but it was not to be, leaving them to focus all their attention on trying to win promotion from League Two, £1m richer from their FA Cup run and with plenty of fond memories to look back on. “I think over the two games we can been very proud of the performances,” Adams said. “I think we’ve put Plymouth Argyle on the map again, we’ve shown a worldwide audience that this football club can get back to where it belongs, and it belongs in the Championship.”