Daniel Sturridge scored the 100th goal of his club career to help Liverpool past a disappointingly flat Huddersfield Town.
The Terriers were still in the game at half-time thanks to Jonas Lössl's save from Mohamed Salah's penalty, but an improved second-half performance from the Reds left the away side, fresh from victory against Manchester United, looking very much second best.
First Sturridge lifted a cute effort over Lössl after a misplaced header from Huddersfield captain Tommy Smith, before Roberto Firmino headed in from a corner a few minutes later.
Georginio Wijnaldum blasted in a third with 15 minutes to play but despite a couple of promising moments in the opening exchanges, Huddersfield never looked like claiming a second famous victory in the space of two weeks.
With Klopp and Wagner in attendance, 'intensity' was always likely to be the word of the day and so it proved from the opening minutes as both sides looked to make a mark on the game.
There was concern for the home side as the Terriers won a pair of corners in the first ten minutes of the game and looked to pack bodies around Simon Mignolet, but some scrappy defending eventually allowed Liverpool to clear.
Early half-chances for Sturridge
Their first chance of the game fell to Sturridge around the quarter of an hour mark. Joe Gomez found him with a deep cross towards the back post, but he mistimed his side-footed effort which bounced up and onto the roof of the goal.
Moments later Liverpool tried the same tactic again and it almost paid off, but Mathias Jørgensen got enough of a touch to knock the ball away from Sturridge as the striker lined up a volley.
Huddersfield were well in the game, particularly on the counter, but other than a couple of threatening runs from Laurent Depoitre and Rajiv van la Parra were struggling to make real headway at the home defence.
Despite this, Klopp's pre-match questions about the state of his defence had hardly been put to bed as Ragnar Klavan, a late introduction at kick-off, looked nervous whenever he was put under pressure by a Huddersfield forward.
With the game ticking on towards thirty minutes, Liverpool perhaps should have been ahead as Salah found a pocket of space from which to shoot after drifting in from the right, but his effort was tame and straight at Lössl.
James Milner had a similar chance from the other side of the penalty area soon after after a raking long pass from Klavan, but Lössl got down well to save after Milner's turn.
Lössl saves from the spot
Just as the home fans were starting to sound some frustrations with their side failing to create a clear goalscoring chance, they were handed exactly that from the penalty spot. Huddersfield captain Smith was booked for shirt-pulling inside the six-yard box after a free-kick, and Salah stepped up to take the spot kick.
It wasn't a good effort. Salah went hard and to the right but his shot was nowhere near the corner, and Lössl didn't have to stretch to first push the penalty clear, then watch Jordan Henderson's rebound wide.
The away end chanted their goalkeeper's name, and the sides went in goalless at half-time. The score was a fair reflection of a well-contested half short on real attacking quality, with both sides missing an effective conduit between midfield and attack.
Sturridge makes his mark
However, it only took five minutes of the second half for Liverpool to earn a stroke of luck. Alberto Moreno's long ball to Firmino was misjudged by Smith and his header played in Sturridge, who lifted the ball superbly over the onrushing Lössl as the Huddersfield captain watched from his knees.
The unfortunate error from Smith seemed to stun the Terriers as Liverpool began to kick into gear for the first sustained spell of the game. Milner's running from deep was instrumental in opening up space where none had existed in the first half, and they had a second goal soon after.
After a superb block in the first half, Jørgensen denied Sturridge a certain goal from Firmino's pull-back across the face of goal, but his work was undone from the resulting corner as Firmino headed hard and low from close range to double the Reds' lead.
With half an hour to play it was Liverpool doing all of the pressing and Salah wasn't pleased to be the only member of the front three without a goal to his name. He held the ball up at the edge of the area apparently waiting for Firmino's run but instead swivelled around his marker and shot, drawing a fine low save onto the post from Lössl.
Wijnaldum strikes for dominant Liverpool
Huddersfield's best chance of the game came from a free-kick at the edge of the area after first-half substitute Elias Kachunga was brought down. Aaron Mooy laid the ball off for Tom Ince to strike, but he curled his effort well over the crossbar.
Emre Can was introduced from the bench to help Liverpool see the game out but Wijnaldum ended any hopes of a comeback with 15 minutes to play. He picked up the ball from Salah at the edge of the area and held onto it for what seemed like an age, before smashing a thundering shot into the near top corner.
Klopp almost had a satisfying end to a satisfying afternoon as substitutes Alex Oxlade-Chamberlain and Dominic Solanke looked to combine, but the striker couldn't get his head to the ball after a surging run around the back of the defence from the former.
Joël Matip headed over the bar when unchallenged from a corner in stoppage time but it didn't spoil Liverpool's afternoon as they moved up to sixth in the table while Huddersfield remained comfortably in mid-table.