This was a clash between two managers who promote a similar brand of football: quick, short passing, clever attacking movement and a high defensive line. But while Liverpool offered possession without penetration and a poor defensive shape, Arsène Wenger's side were impressive when breaking quickly and admirable in their organisation without the ball.

There were two obvious tactical differences between the sides. The first was the level of pressing. Arsenal stood off and focused on getting into an organised shape behind the ball, with two banks of four remaining both narrow and compact, preventing Liverpool playing quick passes through the centre of the pitch.

On the other hand, Brendan Rodgers's side were more energetic when out of possession, closing down high up the pitch. Luis Suárez started the pressure, using his boundless energy to charge towards Arsenal's defenders on the ball. This was more effective when he closed down the right side of Arsenal's defence – Carl Jenkinson and Per Mertesacker were less reliable on the ball than Kieran Gibbs and Thomas Vermaelen and Liverpool won the ball high up the pitch, creating some promising situations in the final third early on.

The second contrast was the format of the three-man midfields. Brendan Rodgers wanted his trio to be fluid – Steven Gerrard, Nuri Sahin and Joe Allen could all, in theory, play in any of the three midfield roles and there was plenty of rotation. If one of the players was high up the pitch and could not receive a simple pass, he would drop deeper to collect the ball, and another midfielder would move higher up the pitch in response.

Arsenal's trio was more structured. Mikel Arteta and Abou Diaby worked as a unit while Santi Cazorla stayed in an advanced position, close to Olivier Giroud. Last week against Stoke, the Spaniard kept dropping deep to help retain possession, which was unnecessary as his role was conflicting with Arteta's. Here he played as more of a classic playmaker.

Whereas Liverpool's three midfielders played short passes in front of Arsenal, Cazorla's positioning meant his side could be more incisive and cut through Liverpool's midfield immediately. The nature of the midfields contributed to the opening goal – Cazorla put himself between the lines and received the ball in space, while Liverpool's midfielders were all high up the pitch. Here, Liverpool missed Lucas Leiva – the Brazilian is an expert at positioning himself intelligently in that zone, defending the width of the pitch by himself.

Cazorla exploited Liverpool's weakness between the lines excellently, and although he was nominally playing in the centre of the pitch, he was especially prominent because of his willingness to move into wider positions to receive the ball in space. He added the second after a run from a central position towards the left, around the outside of the Liverpool central midfielders into a position where no one took responsibility for tracking him.

Cazorla first emerged at Villarreal, where he was used as one of the central attacking midfielders in a 4-2-2-2 system, encouraged to create centrally yet also provide width when needed. He has retained that habit for lateral drifts and this will be vital in Arsenal's linkup play this season, helping to form triangles and keep the passing quick and purposeful.

The tactical battle barely changed as the game went on; the onus was on Rodgers to transform the match, but his bench was particularly uninspiring. Stewart Downing – who Rodgers has said may be used at left-back this season – was the closest to an attacking option. Arsenal's shape remained consistent and they collected their third consecutive clean sheet.

Ferguson searches for right combination

With no central midfielder signed in the transfer window, Sir Alex Ferguson is still trying to find his best combination in the centre of the pitch. In the 3-2 win over Southampton, Tom Cleverley and Michael Carrick were paired together, but both Ferguson and hat-trick hero Robin van Persie acknowledged that the side's performance really improved when Paul Scholes replaced Cleverley after an hour.

The Carrick-Scholes combination clearly remains United's best when they're in control of a game, but does it have the necessary battling qualities without the ball? It hasn't been a problem in the past, but there's a more attacking tilt to United's play this season – with an extra forward deployed on the wing instead of a wide midfielder, and Shinji Kagawa as the No10 with few defensive responsibilities. Carrick and Scholes will increasingly have to win their own battles in the centre of midfield, and playing a physical attacking midfielder against them might be the best approach for opposition coaches.

Van Persie benefits from heading practice

All three of Van Persie's goals came following crosses from wide areas into the penalty box, and Manchester United have played 96 crosses so far this season, more than any other side in the league. Their closest challengers are Newcastle, who have attempted 75.

Van Persie's winner was scored with his head, an area of this game he's put effort into improving over the past couple of years. At the start of 2011, realising that his role at Arsenal was now that of an out-and-out striker, Van Persie stayed behind after training each day to practise his heading, making him more of an all-round goalscoring threat and developing a good relationship with Theo Walcott. He's not a player you'd naturally associate with getting on the end of high balls, but his movement across defenders and pure heading technique has become excellent, so Antonio Valencia's old-fashioned touchline-hugging wing play won't go to waste this season.