There’s always a danger this early in the Premier League season of reading too much into a single set of games. Titles may be lost in September but they are very rarely won. This past weekend, though, did feel like one where many of the prevailing narratives crystalised as Arsenal dug deep to win the sort of game they’ve become used to losing, Liverpool’s defensive shortcomings were exposed as they lost for the first time this campaign, Manchester City swept aside lesser opposition in the manner of old and Chelsea fell apart again.

Liverpool have looked defensively shaky all season. Having been the team of control in the last campaign, making the unremarkable 2-0 win a trademark, they have become the side of the late winner, clinching games this season in the 88th, 94th, 100th, 83rd, 95th, 92nd and 85th minutes. That was never going to be sustainable, but the question was whether general performances would improve, or whether the late strikes would dry up.

The 4-2-3-1 shape with Florian Wirtz playing centrally behind a striker was gone this weekend at Crystal Palace, with a return to the 4-3-3 of last season and Wirtz deployed on the left. That had seemed to add stability when it was used in the second half against Atlético Madrid in the Champions League, the Ryan Gravenberch – Alexis Mac Allister – Dominik Szoboszlai trio of last season returned to their positions. But it is not a quick fix; vulnerability has crept into Liverpool and Palace exposed it again and again, particularly before half-time. As so often under Arne Slot, Liverpool improved after the break, but it’s no exaggeration to say they could have been 3- or 4-0 down by then.

The squad, as it did last season, still looks short of a defensive midfielder, but that does not explain why, even with the familiar three in the middle, Liverpool are so much more open than last year. Trent Alexander-Arnold’s significance, inverting from right-back, adding another degree of central security, has perhaps been generally underestimated. Five wins out of five at the beginning of the season, particularly when one of those games was at home to Arsenal and one away to Newcastle, is a great start. But until Saturday, results had outstripped performances. If Liverpool are to retain their title, at least some of last season’s control needs to return.

Arsenal have made a recent habit of failing to take opportunities but, after last week’s injury-time equaliser against Manchester City there came an injury-time winner against Newcastle to cut the gap at the top to two points. It wasn’t just about the result, though; it was also about overcoming the setback of VAR controversially overturning a penalty decision for them in the first half. Arsenal have over the past couple of seasons become a side with a tendency to get down on themselves, to react badly to misfortune or adversity; that happened to an extent at St James’ as early momentum was lost, but they still had enough to claim the win. Certainly the table looks – and the mood feels – very different now to how it would have done without the late goals in their last two games.

A further three points back are Manchester City, who are at an uncertain stage of their development. They’ve lost twice already in the league and the low block they deployed in the draw at Arsenal was without precedent in Pep Guardiola’s time as management, but they have at least rediscovered the ability to sweep aside lesser opposition at home. Having beaten Manchester United comfortably – albeit with a more counterattacking approach than has been familiar – they followed up a comfortable win over 10-man Napoli with the sort of demolition of Burnley that used to be routine. Perhaps they were more reliant on an individual in Jérémy Doku than would once have been the case, but as they ran in late goals against opponents exhausted by an afternoon of chasing, it was possible to see something of the old swagger returning.

Chelsea are just two points behind City but mired in self-doubt. Their only good league performance this season was in the 5-1 demolition of a compliant West Ham; otherwise they have seemed heavily reliant on Cole Palmer for creativity and, perhaps explicably given their injury issues, shaky at the back. There’s no real excuse in the fact that their two league defeats have come after having a man sent off; both red cards were for the denial of a goalscoring opportunity, one after a simple flick-on and the other after a player was caught in possession. Defensive shortcomings led to the red cards rather than being the result of them. Chelsea may be world champions but at the moment they are miles off a domestic title challenge.

All of the main contenders, in truth, look flawed: Liverpool too open, Arsenal still distrustful of their own abilities and overly reliant on set-plays and City are still integrating new players and adjusting to Guardiola’s new outlook. None of those three look far from clicking – the same cannot be said of Chelsea – but after this weekend, it’s probably Arsenal with the most reason to feel satisfied.

• This is an extract from Soccer with Jonathan Wilson, a weekly look from the Guardian US at the game in Europe and beyond. Subscribe for free here. Have a question for Jonathan? Email soccerwithjw@theguardian.com, and he’ll answer the best in a future edition.