The result means Chelsea, who looked out of contention for a top-four finish just a month ago, picked up their fourth straight league win at the ideal time to apply the pressure.
The spotlight at Stamford Bridge was on league top scorer Mohamed Salah, facing his old club, but the Egypt forward was booked for diving and had a quiet afternoon - one that was understandable in the circumstances, according to Klopp.
Their revered first-choice attacking trio of Salah, Roberto Firmino and Sadio Mane all start, as they did in Wednesday's 4-2 Champions League defeat at Roma, despite the latter suffering a slight knock.
On the hosts' front, Marcos Alonso is back from his three-match suspension while David Luiz and Ethan Ampadu are out from the game.
Eden Hazard was becoming more influential for Chelsea and almost added a second for the hosts after dancing past three Liverpool defenders, his near-post effort just rebuffed by Karius and with 10 minutes to go Marcus Alonso's spectacular left-foot volley whistled just past the post. The Blues were also dumped out of the League Cup and Champions League at crucial intervals of the tournaments by Arsenal and Barcelona respectively.
Amber Rudd makes first backbench speech for six years
In a series of weekend Twitter messages, Rudd said she was unaware of the memo but admitted she should have known of the targets. Mr Javid has also declared plans to put his "own stamp" on the Home Office.
The Reds will be without Adam Lallana, that despite being back to full training, will not be ready for the game on Sunday.
But back-to-back draws with West Brom and Stoke, as well as well-fought victories for Chelsea against Southampton, Burnley and Swansea, have made things hard for Liverpool.
Rudiger's fine display is something that fans have come accustomed to this season, but Tiemoue Bakayoko put in his first good performance of 2018.
"Chelsea is a similar situation to the [Roma] game - fighting with all they have, they don't have anything to lose", Klopp told Liverpoolfc.com."If we draw it's not good for them; if we win it's not good for them".
Liverpool pressed but Chelsea held on to move within three points of the visitors who are third. "Then we'll see what happens".