The Reds were 4-1 up at the Emirates Stadium with just over an hour played after running riot early on in the second half.
Goals from Alex Oxlade-Chamberlain and Calum Chambers threatened a comeback but Liverpool managed to hold on for an important three points.
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One man stood out for Klopp's side, though: Philippe Coutinho.
The 24-year-old was sensational against Arsenal, scoring two goals and striking a fantastic free-kick for his first.
In the aftermath of Coutinho's display, captain Jordan Henderson has revealed how his Brazilian teammate can reach Lionel Messi and Cristiano Ronaldo's level.
He told the Liverpool Echo: "Messi, Ronaldo and [Luis] Suarez - they are seen as the elite players in world football.
"Philippe has certainly got the talent, the work ethic and the hunger to get into that bracket.
"He's a fantastic player for us. I've seen him develop as a player during his time at Liverpool and he's still only 24.
"If he continues to work as hard as he does and continues to develop like he has done then I'm sure he will be in that bracket before long. He's still very young.
"Hopefully it won't be long before people do regard him alongside the Messis of this world. We have to try to keep him fit and keep him playing like that because he was brilliant against Arsenal.”
Henderson isn't the first person to make such a claim, though, with Emile Heskey also a big fan of Coutinho's.
"I think he's got the ability to [match Messi and Ronaldo]," he told Omnisport, per Goal. "I think he's got just as much ability as them and we've seen it in spurts.
"We need to see it more on a constant level now. His skills are phenomenal. I've seen it when he was at Inter and some of the videos that you see from there in training... Wow. He's a phenomenal player.”
There's no doubting Coutinho's ability and potential but, considering what Messi and Ronaldo have achieved in professional football, he has a long way to go before reaching such a level.
But time is on his side. At 24-years-old, the attacking midfielder is yet to reach his prime and will only improve until he reaches that point.