The England international opened the scoring in the 15th minute, tapping home from close range after a mazy run from Gabriel Martinelli. He then turned provider, setting up Gabriel Jesus for Arsenal's second goal just five minutes later.
Martin Ødegaard extended Arsenal's lead in the 34th minute with a powerful strike from outside the area. Jesus grabbed his brace in the second half, converting a penalty in the 73rd minute before completing the scoring in injury time.
The Hammers were unable to mount a meaningful response to Arsenal's dominance, suffering their second defeat of the season. Gianluca Scamacca missed a golden opportunity to pull one back early in the second half, while Michail Antonio was largely anonymous.
"I'm very happy with the performance," said Arsenal manager Mikel Arteta. "The players showed great intensity and quality. Bukayo Saka was outstanding today, and the whole team was excellent. We're delighted to go second in the table."
West Ham manager David Moyes was disappointed with his team's performance. "We were second best today," he admitted. "Arsenal were too good for us. We need to improve quickly if we want to compete for a top-four finish."
Arsenal will host Fulham on Saturday, while West Ham travel to Brighton. Both teams will be looking to maintain their momentum at the start of the new season.