Liverpool emphatically extended their 100 per cent record to remain top of the Premier League, but for captain Jordan Henderson there are still areas for improvement.
Arsenal, who arrived at Anfield the only other team to have maximum points from two matches, were blown away 3-1 by a powerful, energetic performance.
Despite putting in their best display of the season so far, it was the goal they conceded, which means last season's meanest defence have yet to keep a clean sheet in five outings so far, which had Henderson pausing for self-reflection amid all the praise being lavished on them.
"We knew if we did the right things, played to our strengths, defended really well and were clinical in front of goal, then we'd hurt them," Henderson, who made his 100th Premier League appearance as captain, told liverpoolfc.com.
"We managed to do that, so overall it was a really good performance.
"If we want to be really critical, we're disappointed with the goal. I should have cleared it on the edge of the box.
"But we've got to be delighted with the three points, it's tough in the Premier League. Another great performance."
Arsenal's goal by Lucas Torreira came courtesy of a fortuitous bobble in the area after Liverpool got out of position down their right side late on.
It may have made for a different game, especially if £72million summer signing Nicolas Pepe had put away his one-on-one in the first half on his full Gunners debut, but was ultimately just a source of irritation to Jurgen Klopp and his players.
Liverpool had failed to even come close to the levels they reached last season in the first four matches, but they stepped up to the challenge in the first league meeting with one of their 'big six' rivals.
The pace, power and pressing all returned to as they pinned their opponents back inside the final third for most of the first half, limiting the visitors to breakaways utilising the pace of Pepe, who should have scored at least once from three chances which came his way.
But the effect of building that pressure eventually told just before half-time when Joel Matip, not the most proficient in opposition penalty areas, headed his first Premier League goal in 11 months.
When David Luiz inexplicably pulled on Mohamed Salah's shirt just after the break the Egypt international clinically dispatched the penalty before producing an even better finish from a simple three-pass combination between goalkeeper Adrian, Trent Alexander-Arnold and Fabinho which cut Arsenal to pieces.
It was the sort of move Arsenal, with their containment-first approach, never looked capable of replicating and highlighted the gulf between the two sides.
Victory equalled the club record of 12 successive league wins, set from April to October 1990, and another three points at Burnley next week would not only set a new mark but take Liverpool into the international break top of the table.
Klopp believes this week is a key one for him and his players as, once they return after the internationals, the workload increases significantly as the Champions League and Carabao Cup kick in.
"We have a week to prepare for pretty much the rest of the season," he said.
"I've said it often enough – three games a week means you recover, try to squeeze a couple of minutes out of a session to do some tactical stuff to prepare for the opponent, do set-pieces and then go again. That's it.
"In this week (leading up to the Arsenal game) it was completely different, we liked that and now we have another week like this and I am looking forward to it."
