Sean Dyche applied a 'park the bus' approach to try and fend off the Gunners on Sunday but, ultimately, the visitors' quality prevailed when substitute Trossard brilliantly side-footed the ball into the net after an intricate move.
The win sees Arsenal move level on points with Tottenham and Liverpool in the chasing pack behind leaders Manchester City, while Everton have dropped into the bottom three having only accumulated one point from their first five games.
How the game unfolded
Arsenal, as expected, totally dominated the early proceedings and pinning Everton back into their own half with relative ease. The Gunners thought they had taken a deserved lead on the 20th minute mark when Fabio Vieira slid the ball through to Gabriel Martinelli on the left of the penalty area, and the Brazilian coolly dispatched into the bottom corner of the net.
After a VAR check, however, the goal was ruled out due to Eddie Nketiah being marginally offside in the build up to the goal.
That disallowed goal proved to be Martinelli's last contribution of the game, as the wide player hobbled off injured soon after. An unlucky day for Martinelli, to say the least.
The Gunners would continue to dominate throughout the remainder of the first half, accumulating a whopping 78% possession, but after Martinelli hobbled off they largely failed to find any gaps in a turgid Everton back 10.
Arsenal came out of the traps with an extra spring in their step in the second half, moving the ball much quicker and with much more intent. That added intent led to the first notable strike on goal the Gunners had mustered since the offside goal, with Martin Odegaard cutting in from the right of the box to sting the hands of Jordan Pickford with a venomous strike.
It would take until the 68th minute for the visitors to finally get their breakthrough.
That breakthrough would come following an extremely intricate piece of passing play by the Gunners in and around the penalty area which culminated in Bukayo Saka pulling the ball back into the path of Leandro Trossard, who subsequently was able to guide the ball beautifully into the far corner of the net.
It was very nearly 2-0 ten minutes later when Arsenal broke forward quickly in numbers. The effort on goal that this break culminated in proved to be one from Odegaard which was well saved.
Everton player ratings
GK: Jordan Pickford - 6/10 - Could do nothing about the goal. He didn't have a gigantic amount to do otherwise, making two decent saves of relative note.
RB: Ashley Young - 6/10 - Struggled up against Martinelli's runs in behind early on, but generally dealt with Trossard well when he can on.
CB: James Tarkowski - 6/10 - Got his head on a lot of crosses into his box.
CB: Jarrad Branthwaite - 6/10 - A solid outing from the young defender. He's a typical Dyche defender, and that'll mean he'll continue to get gametime for Everton.
LB: Vitaliy Mykolenko - 6/10 - Worked hard up against Saka, but the starboy's quality eventually told.
RM: Dwight McNeil - 4/10 - Basically played as a right-back.
CM: Idrissa Gana Gueye - 4/10 - Struggled to get near the Arsenal midfield.
CM: Amadou Onana - 4/10 - Didn't get his foot on the ball in midfield.
AM: Abdoulaye Doucoure - 4/10 - Barely touched the ball.
LM: Arnaut Danjuma - 4/10 - Everton weren't exactly set up to get anything out of their attackers on Sunday.
ST: Beto - 5/10 - Starved of service.
Substitutes
SUB: Dominic Calvert-Lewin (65' for Beto) - 5/10 - Didn't have much of a hope in this Everton set up.
SUB: James Garner (80' for Doucoure) - N/A
SUB: Nathan Patterson (87' for Young) - N/A
SUB: Youssef Chermiti (88' for McNeil) - N/A
Manager
Sean Dyche - 3/10 - Hard to break down but, ultimately, do fans not want to see their team try and win a game of football? Yes. Did Dyche set up to do that? No.
Arsenal player ratings
GK: David Raya - 5/10 - Possibly the easiest debut in footballing history.
RB: Ben White - 6/10 - Saw a lot of the ball due to his inverted full-back role.
CB: William Saliba - 5/10 - Everton offered nothing going forward, so he didn't have much to do.
CB: Gabriel - 5/10 - Like Saliba, Gabriel had very little to do.
LB: Oleksandr Zinchenko - 6/10 - Looked nearer to his best this weekend.
CM: Martin Odegaard - 6/10 - Saw two efforts on goal saved by Pickford and created three 'chances' for his teammates.
CM: Declan Rice - 6/10 - Kept things ticking over in midfield well.
CM: Fabio Vieira - 6/10 - Provided a bit of creativity that Havertz hasn't in the same position thus far this season.
RW: Gabriel Martinelli - N/A - Scored an offside goal and then went off injured. A snake bit game for Martinelli.
ST: Eddie Nketiah - 5/10 - He didn't really get involved enough.
LW: Bukayo Saka - 7/10 - Assisted what proved to be the winning goal, and enjoyed a very competitive battle against Mykolenko on the day.
Substitutes
SUB: Leandro Trossard (23' for Martinelli) - 8/10 - Scored a wonderful winning goal.
SUB: Gabriel Jesus (66' for Nketiah) - 6/10 - Busy when introduced.
SUB: Kai Havertz (80' for Vieira) - N/A
SUB: Takehiro Tomiyasu (80' for Zinchenko) - N/A
Manager
Mikel Arteta - 6/10 - His team simply didn't move the ball quick enough in the first half, but ultimately found a breakthrough in the second half. The decision to drop Havertz for Vieira proved to be a good one.
