Trossard and Declan Rice struck in the closing stages to secure a vital three points.
Chasing their first title since 2004, the Gunners will pray for a shock City stumble against Wolves at the Etihad Stadium.
Pep Guardiola’s team, who have two games in hand on Arsenal, can clinch an unprecedented fourth successive English title if they win their last four matches.
Arsenal’s 26th Premier League victory this season equalled the club’s top-flight record for a single campaign.
Arteta’s men gifted the title to City last season after a blowing an eight-point lead in the closing weeks.
But the north Londoners have learned from that meltdown, winning 14 of their 16 league games in 2024 to stay firmly in the hunt.
Arsenal travel to Manchester United in their penultimate game next weekend before hosting Everton in what they hope will be a potential title clincher on May 19.
Arteta was a childhood friend of Bournemouth boss Andoni Iraola back home in Spain, but there was no room for sentimentality with the title on the line.
Bournemouth keeper Mark Travers was destined for a busy afternoon and it wasn’t long before he made his first save to deny Kai Havertz from a tight angle.
Trossard delivers
Even Arsenal defender William Saliba was willing to rumble forward, cleverly cutting back to find space for a shot that Travers saved at his near post.
Travers repelled a stinging strike from Saka, with Takehiro Tomiyasu’s effort cleared off the line from the resulting corner.
Unmarked 10 yards from goal, Declan Rice lashed narrowly wide from Havertz’s knock down, a miss that left anxiety and frustration etched all over Arteta’s face.
Arteta could finally relax in the 45th minute when Havertz left his leg dangling to ensure he was tripped by the slightest contact from Travers as the German skipped around him.
Saka stepped up to calmly slot the penalty down the middle for his 20th goal in all competitions this season.
Saka should have doubled Arsenal’s lead soon after half-time, but his scuffed close-range shot from Havertz’s pass was straight at Travers.
Arsenal couldn’t rest on their laurels with a one-goal lead and Dominic Solanke nearly caught them out as the Bournemouth striker forced David Raya to save.
Havertz’s low drive was stopped at full stretch by the over-worked Travers, but Bournemouth’s Justin Kluivert went close with a shot that dipped just over.
Trossard finally delivered the knockout blow in the 70th minute, running onto Rice’s pass and slotting a clinical finish past Travers from 12 yards.
Bournemouth’s Antoine Semenyo had a goal harshly disallowed for a soft challenge by Solanke on Raya.
But Rice blasted home from close-range deep into stoppage-time as Arsenal cruised to a victory that kept their title dreams alive.
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