After suffering Europa League quarter-final heartbreak to Atalanta BC and suffering a shock Premier League home loss to Crystal Palace, the Reds comfortably got back on track in West London.
A sublime Trent Alexander-Arnold free kick opened the scoring on Sunday afternoon, but Marco Silva's side fought back before the break through their own right-back, as Timothy Castagne arrived on the scene to find the bottom corner.
Only the top six sides in the division had performed better at home than Fulham heading into the weekend, but Klopp's men were a class above in the second period and deservedly prevailed thanks to Ryan Gravenberch's stunning strike and a Diogo Jota finish.
Vice-captain Alexander-Arnold was surprisingly named in the starting XI after an energy-draining night against Atalanta in the Europa League, but the defender's selection was justified, and he now sits on six free-kick goals for Liverpool in the Premier League.
Klopp hails unique Alexander-Arnold after Conor Bradley emergence
Only Jamie Redknapp (eight) and Steven Gerrard (seven) have managed more for the Reds in the competition, and Klopp was overjoyed to have Alexander-Arnold back in the XI, despite the breakthrough of 'shooting star' Conor Bradley.
Asked in his post-game press conference about the importance of Alexander-Arnold's return to the starting lineup following a pair of knee injuries, Klopp responded: "It's super-important. Super-important.
"But, for example, one of the shooting stars of this season is Conor Bradley, who played the position and he played in a few games football where we all thought, 'Oh, wow... what was that?!' But nobody is like Trent. Nobody is like Trent.
"The way we play with him can be different, so yes, it is super-helpful and I am really happy about that. For a long period of time Trent was exceptional, super-helpful to have him back. Yeah, top."
Despite going into the tunnel level at half time, Liverpool faced a far more meek Fulham side in the second half, where Gravenberch's stunning curler preceded Jota's 100th goal in English football, and his 56th for the Merseyside giants.
Klopp makes 'obvious' best finisher admission after Jota claim
The Portugal international enhanced his reputation as a clinical finisher at Craven Cottage and is averaging a goal once every 115 minutes in the Premier League, the best rate of any player with at least five non-penalty strikes.
Even though Jota - whose start against Fulham was his first since suffering a knee injury in February - boasts the best big-chance conversion rate of all of Liverpool's attackers, Klopp was quick to shoot down the idea that the ex-Wolverhampton Wanderers man is the best finisher at the club.
"The best finisher in this club is obviously Mo [Mohamed] Salah with some distance," Klopp added. "It is just super-cool to have Diogo back, he can play all three positions up front."
By returning to winning ways in the capital, Liverpool have risen above Manchester City into second place in the Premier League table behind Arsenal, who are only leading the way on goal difference.
Klopp's side now have the small matter of a Merseyside derby with Everton at Goodison Park on Wednesday, before kicking off the weekend's action away to West Ham United on Saturday lunchtime.