We came from behind for the third consecutive game to win for the third consecutive time.
Swansea drew first blood when Tammy Abraham took advantage of Laurent Koscielny’s slip to play in Sam Clucas for a low finish past Petr Cech.
Our first-half performance was sluggish by recent standards, with lots of possession but not much penetration. A brilliant tip-over from Lukasz Fabianski to deny Alexis was the closest we came to a goal.
But we raised the tempo after the break and turned the game on its head.
The equaliser came when Alex Lacazette showed strength to keep a move alive and then flair to find Mesut Ozil with a backheel inside the box. The German’s shot hit a defender but the ball rolled kindly for Sead Kolasinac, who flashed a first-time shot inside the far post.
The Bosnian turned provider eight minutes later. Granit Xhaka’s raking pass picked out Kolasinac and he picked out Ramsey’s run for another first-time finish past former Gunner Fabianski. It was Ramsey’s 50th goal for us.
Hector Bellerin saw a shot clip the crossbar and substitute Olivier Giroud found the side-netting, but we’d done enough.
There were groans around Emirates Stadium at half-time but smiles of satisfaction at the final whistle. Three more points to mark Arsene Wenger’s 800th Premier League game - and valuable momentum ahead of next weekend’s trip to Manchester City.
AS IT HAPPENED
WHAT IT MEANS
This result leaves us in fifth place in the Premier League, after Chelsea beat Bournemouth 1-0 in Saturday's late kick-off.
We remain nine points behind our next top-flight opponents, Manchester City.
The competition changes again in midweek as we move from Premier League to Europa League, and the visit of Red Star Belgrade.
A positive result will secure our place in the knockout stage.
Next up in the Premier League is a trip to leaders Manchester City - our final game before the next international break.
Alexis took the fight to Swansea City in the first half, when he was probably our most dangerous player.
He faded slightly in the closing stages but here are Alexis’ best moments:
6 - After a stepover to the right and a stepover to left, Alexis fizzes in low cross but Fabianski grabs it
8 - Tightly marshalled just inside the box but he gets away from his marker and exchanges passes with Lacazette before Swansea clear
10 - A ball over the top finds Alexis running in behind but he can’t quite get his first touch right and Fabianski is there
18 - Alexis takes aim from just outside the box, but his shot flies wide of the near post
20 - A sharp turn on the left allows Alexis to slide a ball into the channel for Kolasinac, but Swansea defend well
32 - Alexis takes matters into his own hands with a darting run from left to right, but Abraham stops him
37 - Alexis spots Ozil’s run into the box and curves in a cross - but it just misses its target
41 - Slick interplay between Kolasinac and Alexis gives the latter room for a ferocious shot, but Fabianski tips over brilliantly
55 - Alexis curls in a perfectly-flighted free-kick but Koscielny can’t direct a free header on goal
72 - Ramsey’s short pass finds Alexis in space but he shoots well over from 20 yards
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