We overcame sub-zero temperatures on an artificial pitch to secure a healthy first-leg advantage in the Europa League round of 32.
On our first trip to Sweden since 1999, goals from Nacho Monreal , Mesut Ozil and an own goal - with Henrikh Mkhitaryan providing two more assists - have put us firmly in control of this tie. David Ospina's late penalty save also preserved a welcome clean sheet on the road.
The Swedes, managed by Englishman Graham Potter, were unbeaten at home in six Europa League games so far this season, but the Gunners were too strong on the night and we are firm favourites to progress now.
After finding our feet on the artificial surface, passing the ball around while the hosts camped out in their own half, we took the lead inside the opening quarter of an hour.
Monreal was the goalscorer - keeping up his recent hot streak in front of goal. He was on hand to finish from close range after Alex Iwobi's shot was spilled by goalkeeper Aly Keita. It was the left back's fifth goal of the campaign - he had only scored three in his time at the club prior to the start of this season.
Danny Welbeck had already seen a header go wide from close range, while Mkhitaryan had a goalbound shot cleared off the line by the diving defender Sotirios Papagiannopoulos.
It was one-way traffic in the first half hour, with us enjoying nearly 80 per cent of the possession.
The second goal was on the cards, and Mkhitaryan was the architect. His low cross was turned into his own net by Papagiannopoulos, under pressure from Welbeck.
The hosts were now forced to abandon their defensive approach, and started making chances of their own. Ospina - captain for the night - saved well from Saman Ghoddos then held a Ken Sema free-kick.
We extended our lead just before the hour mark. Ozil exchanged passes with Mkhitaryan, burst into the box, then squeezed his shot just under the keeper.
The pace of the game slowed after the third goal - youngsters Eddie Nketiah and Reiss Nelson were introduced for the final ten minutes or so.
We were dictating the tempo now and Ostersunds - who are still in domestic pre-season - were tiring.
Right at the end, the hosts had a chance to score on what was the biggest match of their 21-year history.
Hector Bellerin conceded a penalty in stoppage time, bringing down Tesfaldet Tekie, but Ospina dived to his right to save Tom Pettersson's low spot kick.
The job is half-done - now to complete the task in London next week.
What it means
We take a commanding lead into the second leg, with three away goals to boot. It means we are well placed to progress to the last 16 of the competition.
We don't play again until the return match at Emirates Stadium next Thursday. That game kicks off at 8.05pm and comes just three days before the Carabao Cup final against Manchester City at Wembley.
With Alexandre Lacazette injured and Pierre-Emerick Aubameyang ineligible for the Europa League, the attacking spotlight fell on Danny Welbeck. Here are some of the England man's best moments.
8 - Danny has our first effort on goal, but his close-range header floats wide
25 - Welbeck was the closest to Papagiannopoulos inside the area when the Ostersunds defender turned Mkhitaryan's cross into his own goal
34 - After being set up by Iwobi on the counter attack, Welbeck fired well over from a wide angle
71 - Often drifting wide, Danny tees up Nacho Monreal in the box, but the defender's shot is charged down
81 - Just before being brought off, Welbeck curls a shot from 20 yards just wide of the post
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