The Belgium international’s second league goal for the club he joined in January was a paltry return for the dominance the Gunners enjoyed but it proved enough to halt a sequence of four defeats and a draw in L4.
For a team who enjoyed so much possession, Mikel Arteta’s side created very little with it until Trossard’s 69th-minute breakthrough – highlighted by starting centre-forward Eddie Nketiah’s paltry 10 touches before he was withdrawn three minutes before the goal.
Arsenal will have wished he had one fewer as it was his lay-off returning from an offside position which resulted in Gabriel Martinelli’s first-half goal being ruled out for offside.
On-loan Brentford goalkeeper David Raya was similarly underemployed having been handed his debut as part of Arteta’s rotation policy between the posts and the manager will not have learned much about his fellow Spaniard against an Everton side short on shots and attacking intent.
However, squeezing out a win on a ground which has recently proved a huge stumbling block for the north Londoners will have at least given the Gunners boss some satisfaction and the travelling support sang their appreciation of a scoreline with which they have become synonymous.
Not so his Everton counterpart Sean Dyche, whose side have now lost all three home matches this season, have only one point and remain in the bottom three and facing a third successive relegation dogfight.
While they posed little realistic threat, they did not do much wrong in frustrating their opponents for long periods and the return of Dominic Calvert-Lewin as a second-half substitute and winger Dwight McNeil starting his first game of the season should offer some grounds for optimism.
But with only two goals, both scored at Sheffield United immediately before the international break, and with summer signing Beto showing every inch of the “rawness” Dyche claimed he had, something has to improve up front.
But desperation was started to show on the hour when the players frantically appealed for handball after Oleksandr Zinchenko’s drive from distance hit the diving James Tarkowski but his arm was tucked into his body.
Both managers decided a change of strikers was what needed to change their luck in the 66th minute and Calvert-Lewin – wearing a protective mask after a recent facial injury – and Gabriel Jesus arrived at the same time.
But it was first-half substitute Trossard who made the difference from an Arsenal short corner.
The ball was worked between Zinchenko and Odegaard to Bukayo Saka whose cutback was cleverly steered in left-footed via the far post by the Belgian for his first goal since February.
However, it was not much of an improvement on a forgettable first half, in which Everton matched the visitors for shots on target (one) despite having only 20 per cent possession, and the only real talking point was Martinelli’s disallowed 19th-minute goal.
Beto, making his home debut, charged down Gabriel and the ball rebounded to Nketiah, who laid off to Fabio Vieira to thread a pass in for his team-mate to curl a shot past Jordan Pickford only for VAR to chalk off the effort.
It was Martinelli’s last involvement as injury forced his replacement by Trossard.
Abdoulaye Doucoure wanted a penalty after breaking from midfield, lobbing Declan Rice, and cutting inside onto his right foot only to be clipped by William Saliba but referee Simon Hooper saw no infringement.