It's never easy to get three points at Selhurst Park.
Crystal Palace jostled and fought valiantly against Liverpool but their work was undone shortly before half-time when Mamadou Sakho clipped Mo Salah inside the box.
James Milner scored the resulting penalty and things got even worse for the hosts with a quarter of an hour left, 20-year-old Aaron Wan-Bissaka seeing red.
Just as it looked as if Palace might have grabbed a last-gasp equaliser, Sadio Mane hit them on the counter to make it 2-0.
The Reds had squandered chances to double their lead earlier on. They weren't quite as clinical as they had been in their ruthless thrashing of West Ham a week earlier.
Salah and Mane both missed opportunities to put the game to bed, though Jurgen Klopp is unlikely to lose any sleep over it.
Instead, the German must have been very pleased with most of what he saw. Alisson Becker secured another clean sheet and Naby Keita put in a masterclass in midfield.
The Guinea international has the perfect balance of aggression and in-game intelligence, at least judging by his early displays for the club.
Against the Eagles, he was wonderfully adept, pulling the strings and covering an awe-inspiring amount of ground.
Crucially, he seemed to combine very well with Salah, last season's Golden Boot winner, and that is what has got Liverpool fans excited.
Keita looks a fantastic signing
On one occasion, Keita glided away from Andros Townsend with a neat bit of skill before sending a perfectly-weighted ball over the top to the Egyptian.
Salah wasn't able to put the chance away, but even so - glorious:
On a night when Fabinho was left out of the squad, his fellow new signing looks to be having no such troubles adapting to English football.
"Naby, we all have no clue how good he can be,” Klopp had said in his pre-match press conference.
“He's too young to judge him. What can we say? Obviously he learned very quickly already in the last few years, from Austria to Leipzig, now here.
“So he adapts constantly and brings himself to the next level. Adapts to the other players, uses them really well."
Keita and Salah already look like a deadly combination.
What did you make of Keita's performance? Have your say in the comments.