Still suffering a hangover from their 4-1 loss to Tottenham last Sunday, a lethargic home side struggled to break down resolute opponents during an opening half that saw Huddersfield goalkeeper Jonas Lossl keep out a Mohamed Salah penalty.
However, Daniel Sturridge eased the simmering tension inside Anfield five minutes after the interval, capitalising on an error by Tommy Smith to break the deadlock and score his 100th goal in club football.
Roberto Firmino made it 2-0 eight minutes later, the Brazilian heading home a James Milner corner to give Liverpool breathing space in the first league meeting of the two clubs since 1972.
Georginio Wijnaldum added a third as Huddersfield, who have still not won away since the opening weekend of the campaign, were bought back down to earth with a bump following their shock 2-0 home win over Manchester United a week ago.
After facing questions over his team's defensive frailties following their collapse last Sunday, Klopp initially intended to keep faith with the same back four who started last time out, only to be forced into a late change.
Withdrawn just 31 minutes into the game at Wembley Stadium, Dejan Lovren failed to even make it to kick-off this time, the much-maligned centre-back ruled out after picking up an injury while warming up.
Wagner had embraced Klopp on the touchline prior to the start but showed no willingness to help out his compatriot with his tactics, setting up the visitors to defend deep and frustrate their opponents.
The policy worked during an opening half that saw Liverpool's players produce little to lift a subdued home crowd.
They were handed the chance to go ahead three minutes before the break when Smith's blatant shirt pull on Firmino at a corner was spotted by referee Kevin Friend, only for Lossl to guess correctly and keep out Salah's driven penalty.
Huddersfield's club captain was still involved in the opening goal, however, as his attempt to head clear a long ball inadvertently teed up Sturridge, who expertly chipped the advancing Lossl in front of the Kop.
The England international missed out on his 101st club goal when Mathias Jorgensen's desperate sliding clearance prevented him from tapping home, although Liverpool did not have to wait much longer for their second.
From the resulting corner, Milner's inswinging delivery picked out the run of Firmino, who evaded marker Aaron Mooy to plant a close-range header through Lossl and into the net.
After Joel Matip came close to converting from another set-piece opportunity, Wijnaldum rounded out the scoring in the 75th minute with a rising, right-footed shot that flashed high into the top-right corner.Able to enjoy the closing stages, Klopp celebrated the much-needed victory by planting a kiss on the cheek of opposite number Wagner after the final whistle, showing that while the battle between the two Germans was one-sided, the bond between the two former Mainz colleagues remains strong.
18 - All 18 of Georginio Wijnaldum's @premierleague goals have come in home games (11 St James' Park, 7 Anfield). Castle.— OptaJoe (@OptaJoe) October 28, 2017
Key Opta stats:
- Liverpool have lost only one of their last 43 Premier League home games against newly-promoted sides (W33 D9).
- Huddersfield have failed to score in four consecutive away league games for the first time since October 2007, when they were in the third tier (5 games in that run).
- No side has missed more Premier League penalties than Liverpool (34, level with Arsenal).
- Salah has registered 12 goal involvements in all competitions for Liverpool this season (9 goals, 3 assists), more than any other player for the Reds.
- Daniel Sturridge netted his 100th goal in club competition (62 Liverpool, 24 Chelsea, 8 Bolton, 6 Man City).
- Roberto Firmino has scored 24 Premier League goals, more than any other Liverpool player since his debut in August 2015.
- Georginio Wijnaldum's haul of 18 is the most goals exclusively scored at home by any player in Premier League history.