Both sides started brightly but it quickly became clear that Arsenal were going to have more of the possession as the moved the ball around at lightning speed.
Mohamed Diame then struck against the run of play to give the Hammers the lead after 21 minutes.
The Hammers would have been hoping to hold onto that lead until half-time but were pegged back by a goal from new-boy Olivier Giroud.
In the second half Arsenal were much the better side but the Hammers were still finding themselves with good chances to take the lead.
It wasn’t until the 77th minute that substitute Theo Walcott latched onto a through-ball and calmly slotted the ball past Jaaskelainen to send the Gunners into the lead.
Arsenal then secured all three points with a fine striker from Santi Cazorla.