Swansea's fourth consecutive league defeat added up to its worst start to a season in any division with just four points from its eight games.
Arsenal, meanwhile, moved even on points with league leader Manchester City, trailing Pep Guardiola's club on goal difference.
The in-form trio of Alexis Sanchez, Ozil, and Walcott continued to produce the sort of passing and movement that opposing defenses have struggled to cope with. Arsenal made its early territorial dominance pay in the 26th minute as Sanchez's looping pass found Hector Bellerin on the right of the box. He headed down the ball for Walcott to poke home — only after Jordi Amat and Lukasz Fabianski wasted opportunities to clear.