The Reds earned a 2-1 win at Wembley against Tottenham, while Maurizio Sarri's side came from behind to thump Cardiff City 4-1 at Stamford Bridge, thanks to an Eden Hazard hat-trick.
Georginio Wijnaldum picked a good time to score his first away goal in the Premier League when he headed Liverpool into a 39th-minute lead, before Roberto Firmino steered home a second early in the second half to ensure Liverpool made it five wins from five.
Erik Lamela grabbed a late consolation for Spurs, who could not avoid a second straight Premier League defeat.
"Tottenham are not really happy at the moment with the result and not with the performance, but because we were that good it was so hard for Tottenham". We need to improve a lot. "We could have scored more and we controlled the game".
4 dead as Hurricane Florence drenches the Carolinas
People in the Carolinas had the daytime hours Thursday to complete their final preparations to ride out or escape the storm. At least 12,000 people had taken refuge in 126 emergency shelters, Governor Cooper said, with more facilities being opened.
Four wins from four in the opening stretch of the season spoke well of Liverpool's ambitions without them ever quite hitting top gear, but the relative ease with which they dispatched Spurs counts as a statement. Klopp told reporters before Liverpool's game against Spurs (via ESPN). "We all knew it after the World Cup, especially after England came that far, they have had no rest", added Klopp.
Meanwhile, the Liverpool manager is unsure on the severity of Firmino's facial injury that forced him off in the 74th minute on Saturday following a duel with Jan Vertongen.
"We have, I'm not sure, but maybe an injury with Roberto".
The Reds' next assignment is a Champions League clash against Paris Saint-Germain on Tuesday, with both clubs boasting ideal records to date this season. "I see the game and I talk here and analyse it and then I don't think too much about it anymore, to be honest", he said.
"A hospital examination confirmed an abrasion of the eye, but there will be no lasting damage".