Reports of Guardiola’s imminent departure overshadowed the build-up to a potentially tricky assignment, as City looked to take the PL title race to the final day.
They created their first opening when Antoine Semenyo raced down the right-hand side and teed up Jeremy Doku, whose left-footed effort was comfortably saved by Dorde Petrovic.
Semenyo then slotted the ball in the back of the net against his former club, but was denied by the linesman’s flag.
Evanilson would then have been disappointed to blaze his close-range shot over the bar, only to have his blushes spared by another offside call.
City were doing most of the probing though, and Erling Haaland saw his left-footed strike deflected behind by Evanilson after the Brazilian cleared Rodri’s initial header from Bernardo Silva’s corner.
However, it was Andoni Iraola’s men who struck first with a goal which would have been cheered just as loudly in North London as it was in Dorset. Junior Kroupi took Adrien Truffert’s ball into stride, opened up his body, and curled an unstoppable right-footed effort past a motionless Gianluigi Donnarumma.
The Gunners’ champagne was on ice, but they may have been tempted to put their bottles back in the fridge had Petrovic not made a fine save to deny Nico O’Reilly from deep inside the box just seconds after the restart.
But those City fans hoping this would lead to an onslaught on Bournemouth’s goal were left disappointed.
Surprisingly, the Cherries didn’t defend for their lives – as most teams with a lead over City might – Donnarumma was called into action to parry away Adrien Truffert’s strike, while Kroupi blazed his attempt over the bar from Evanilson’s deft backheel at the end of a sublime passage of play.
Rayan then came within inches of becoming only the fourth teenager to score in four successive PL games when he reacted to James Hill’s knockdown with a sliding effort which cannoned off the post.
David Brooks could have added gloss to the scoreline late on, but his shot also hit the woodwork in the closing stages.
To give credit where due, Guardiola’s team did have the final say on the night, restoring parity at the death when Haaland’s angled strike clipped in off the post, but a coveted second didn’t materialise, and the celebrations began at the Emirates.
City's point is firmly overshadowed by the wider context of a title race they have now lost, and the dust will now settle on a campaign of mixed fortunes for a City side which tasted victory in both domestic cup competitions, but missed out on the two biggest prizes available.
Meanwhile, the Cherries can reflect on a season of outstanding progress. They are now undefeated in 17 PL games (W9, D8) and are guaranteed UEFA Europa League football as the bare minimum for next season.
UCL qualification also remains a distinct possibility, though, and would leave Iraola to reflect on an enduring legacy when he departs at the end of this week.