Everton, still without a win this season, had managed to frustrate the visitors who had a Gabriel Martinelli goal ruled out for offside via VAR in the first period.
But the Londoners were eventually rewarded for their domination as Trossard’s shot cannoned in off the post after a clever build-up in the 69th minute.
Unbeaten Arsenal joined Tottenham Hotspur and Liverpool on 13 points from five games, two points behind leaders Manchester City who have a 100% record. A third successive 1-0 home defeat left Everton third from bottom with one point.
Arsenal face a huge week ahead with their return to the Champions League on Wednesday followed by next weekend’s north London derby against Tottenham Hotspur.
Everton might have hoped that Mikel Arteta’s side might have been distracted by those impending dates, but were ultimately unable to live with an Arsenal side that never hit top gear.
Everton offered very little to suggest they will be far away from the relegation strugglers this season with a display high on graft but sadly lacking in quality.
Arsenal’s last league win at Everton in 2017 ended the reign of Ronald Koeman and while Sean Dyche is unlikely to suffer a similar fate, he has a huge task on his hands.
Everton were given a let-off in the 17th minute when Martinelli was played through on goal and finished with a curled finish reminiscent of Thierry Henry in his pomp.
Arsenal’s celebrations were cut short though as a VAR check ruled that there was an offside in the build-up.
For all Arsenal’s possession they were guilty of over-elaboration at times and Everton were hanging on grimly for what would have been a morale-boosting draw.
But Arsenal eventually unpicked their defence with Martin Ødegaard playing in Bukayo Saka on the right side of the penalty area, and the England forward cut the ball back for Trossard who opened his left foot and placed a shot in off the far post.