Victory was a must at Anfield and while Mohamed Salah got them up and running, Mohammed Kudus hammered home a brilliant equaliser ten minutes later.
It looked like Liverpool were going to drop points for the sixth time in eight matches across all competitions this season, but Matip stepped up late on to deliver for his side, his header just about crossing the line.
The win is a much-needed boost for Liverpool, heading into the international break. They are not in action this weekend after their Premier League clash against Chelsea was postponed due to policing issues ahead of the Queen’s funeral.
Klopp had spoken about the need for his side to reinvent themselves after Naples, but his team selection, with midfield still an area of weakness, was more a series of tweaks than anything radical.
His decision to hand Diogo Jota, their pressing machine, a first start since May after injury instead of big-money summer signing Nunez was a deliberate attempt to inject more energy up front in the expectation it would be replicated behind him.
The Portugal international’s early endeavours were matched by Thiago Alcantara, in his first start since the opening day of the season after injury, but his fellow midfielders Fabinho and Harvey Elliott were not quite at the same level.
Jota’s inclusion paid dividends in the 17th minute when, for only the second time this season, Liverpool scored first as he slid an inviting ball into the penalty area for Salah to tuck a left-footed shot past Remko Pasveer.
But the hosts failed to capitalise on that advantage, with Luis Diaz and Jota blasting wide and Salah failing to get enough on a low Jota cross.
They were made to pay in the 27th minute when their right side was exposed as it has been on numerous times already this season.
Trent Alexander-Arnold allowed Steven Berghuis to run beyond him, Elliot did not track back to cover Steven Bergwijn and that allowed the former Tottenham forward to run across the path of Virgil van Dijk to give Kudus the space to lash in a shot off the underside of the crossbar.
Jota and Elliott were replaced by Roberto Firmino and Nunez just past the hour as Liverpool switched to 4-2-3-1, but it actually made things more chaotic as they continued to concede possession in midfield, allowing the unmarked Daley Blind to steer a header across goal and just past the far post.
Nunez rolled a shot wide after good interplay between Firmino and Salah and then the Uruguayan flashed a cross through the six-yard area which was nicked past the waiting Diaz.
But when Salah’s deflected shot looped on to the upright Matip pounced from the resulting corner to get last season’s beaten finalists up and running.
Additional reporting by PA Sport.