Arsenal withstood sustained pressure from West Ham to win 1-0 at the Emirates on Saturday.
Alexandre Lacazette's 78th minute goal was the only difference between the teams on a day when West Ham will be annoyed that they didn't walk away with more.
Lacazette told the BBC after the game: "I'm happy to score for the team. We worked hard. It was a difficult game. I'm happy. They deserved more because of the chances they created. This is football, sometimes you don't get what you deserve.
"It is my job to give the manager a big headache. I'm struggling to make the first team but I'm happy to score again today.
"I know that now I have to play well again the next game. Everyone wants to give their best and it's normal that whenever we do that we will perform as a team."
The Hammers cut a frustrated figure at the end of the first half after they failed to score despite having multiple chances. Granit Xhaka lost the ball to Jarrod Bowen within the first three minutes, and he forced Bernd Leno into an early save.
The first half continued in similar fashion with Michail Antonio and Sebastien Haller spurning chances. Arsenal had flashes of good play and Sokratis Papastathopoulos came close to putting the hosts ahead 23 minutes in. Pierre-Emerick Aubameyang swung a high cross into the box which Sokratis took ahead of Haller but directed just too high to find the net.
Eddie Nketiah made way for Lacazette in the second half and the France international proved to be the difference. There was a VAR check for offside on his right footed shot that blazed into the bottom left corner but the goal counted after a lengthy wait and Arsenal held on to win.