United's display was structured but too much space was afforded to Bacary Sagna, who was a consistent danger

This narrow Manchester United victory demonstrated the fine margins between a strategy being considered successful or naive. David Moyes instructed his side to play extremely narrow, which was highly effective at limiting impact of Arsenal's playmakers, but it afforded space to Bacary Sagna, whose crosses were consistently dangerous in the second period.

Both managers selected cautious starting XIs – Moyes used the tenacious Phil Jones alongside Michael Carrick in midfield, while the absence of Tomas Rosicky forced Arsène Wenger to move Aaron Ramsey wide, with Mathieu Flamini being used in the holding role. It meant both sides played with a double screen in front of their back four, and the creative players were starved of space.

Particularly important in United's triumph was their performance in the opening 10 minutes, when they did not create any chances but enjoyed 67% of possession, much of it inside the Arsenal half. In a match where United were in danger of being overrun in midfield because of Arsenal's superior passing quality, it was crucial United imposed themselves immediately.

Both sides were exceptionally well organised without possession, with Manchester United particularly impressive in the first half. Moyes employed a strategy he often favoured against Arsenal in his Everton days, asking the wide midfielders to drop into deep, narrow positions, cutting off the passing angle into Arsenal's attacking midfielders.

Arsenal have coped well without Theo Walcott and Lukas Podolski this season but here they desperately needed some pace and directness out wide.

Moyes is a very reactive manager, assessing the opposition's strengths and weaknesses and varying his team accordingly. His strategy here was also similar to the approach he used as Everton manager last season against Tottenham – who were without both Gareth Bale and Aaron Lennon, and therefore forced to cope without any true wingers. Everton packed the central positions and happily conceded space out wide – if Moyes knows the opposition lack width, he will force them to play down the flanks.

Something similar happened in the first half here: with Ramsey and Santi Cazorla both moving inside into central positions, Arsenal's attacks were too predictable. Wenger's side lacked sharpness when attempting intricate passing moves and possession was conceded extremely cheaply.

Right-back raider: Manchester United planned to defend narrowly to starve Arsenal's playmakers of space, but gave Bacary Sagna the freedom to attack. Photograph: Guardian

Arsenal's full-backs were given space, which was a risky strategy from Moyes, considering Arsenal have scored plenty of goals from crosses in recent weeks, but in the first half Antonio Valencia and Shinji Kagawa worked hard to close down Sagna and Kieran Gibbs when the play was switched wide. However, the second half showed the dangers of United's approach.

First Ramsey moved wider, taking advantage of the space down the right, and later Mesut Özil was moved to that flank, making clever runs in behind the defence. But the second half's key player was Sagna, rejuvenated this season and consistently dangerous with his delivery from wide – he has created goals in the wins over Napoli and Liverpool.

The Frenchman crossed the ball seven times after the break, creating two chances and whipping two other fantastic balls in behind the Manchester United defence, into the corridor of uncertainty that begged for Olivier Giroud – or another Arsenal attacker – to provide the finish. The absence of Nemanja Vidic, who departed at half-time with a head injury, was clearly a factor in United's uncertain aerial defending.

Moyes became concerned about Sagna's freedom, removing an exhausted Kagawa and introducing Ryan Giggs, with instructions to shackle the right-back, although the crosses kept coming.

In all it was the type of performance we can expect from Manchester United in big matches this season – structured without the ball, cautious when it comes to throwing men forward and reliant on the front two for goals.