Goals from Nacho Monreal and Mesut Ozil helped Arsenal seize control of the
Following a dominant opening 15 minutes, Monreal tapped in the opener after Ostersunds keeper Aly Keita could only parry Mohammed Elneny's effort.
Arsene Wenger made five changes from the Arsenal side that suffered derby defeat to Tottenham on Saturday, with Ospina, Calum Chambers, Ainsley Maitland-Niles, Alex Iwobi and Danny Welbeck all coming into the starting eleven.
With the Swedish football season running on a summer calendar rather than a winter one, this was just the second competitive match of 2018 for the hosts, and English manager Graham Potter made five changes of his own from the side that beat Trelleborgs 3-0 in the Swedish Cup on Friday.
Having perhaps dominated possession and territory as expected in the opening exchanges, it was Welbeck who had the first chance of the game for Arsenal, but the stand in striker headed Elneny's pull back off target from a tight angle seven minutes in.
The Gunners went even closer twelve minutes into the game when Ozil pounced on a weak clearance from Ostersunds keeper Keita, but after his effort beat the goalkeeper, defender Papagiannopoulos was on hand to clear off the line.
Arsenal did however take the lead from their next attack. After Alex Iwobi's first effort bounced back to him off an Ostersunds defender, the Nigerian's tame effort was only parried by Keita, and Monreal was on hand to tap home the rebound to give Arsenal the lead inside the opening quarter of an hour.
5 - Nacho Monreal has now been directly involved in five goals in his last six games for Arsenal in all competitions (three goals, two assists), as many as in his previous 64 matches combined. Surge. pic.twitter.com/9cdUfGe6Gm— OptaJoe (@OptaJoe) February 15, 2018
The visitors continued to press the assault, and Mkhitaryan went close to his first Arsenal goal when his long range effort was beaten away by Keita.
Just after the midway point of the first half, Arsenal doubled their lead, as Mkhitaryan's cut back was inadvertently deflected into his own net by Papagiannopolous after the Swedish side's defence had initially failed to clear Bellerin's run and cross into the area.
The concession of a second goal finally sparked some life into the hosts, and Ghoddos came close to pulling one back as his fizzing effort from the edge of the area was tipped over the bar by Ospina.
With Ostersunds suddenly pressing for a famous goal, Arsenal came close to snatching a third on the counter, but having broken into the Ostersunds area, Bellerin's pass across the face of goal was curled well over by Welbeck.
Apparently unfazed by Arsenal's counter attacking threat, Ostersunds continued to press forward, creating a couple of half chances as Sema hit a twenty yard free kick into the arms of Ospina before Ghoddos drove low and wide from even further out in the final five minutes of the opening half.
At the other end, Mkhitaryan again missed a chance for his first Gunners goal, striking high and wide from inside the area in first half stoppage time.
Having soaked up another spell of Ostersunds pressure at the start of the first half, it was Arsenal who fashioned the first half chance of the second period, as home keeper Keita needed the assistance of defender Papagiannopolous after he could only parry a cross from Elneny.
There would be no help for Keita moments later as Arsenal all but put the tie to bed when Mesut Ozil made it 3-0 to the Gunners. Playing a one-two with Mkhitaryan, the German was able to make his run into the area, and despite Keita getting a touch on his shot, the ball trickled over the line to give Ozil his fifth goal of the season.
With Arsenal now in cruise control and Ostersunds struggling to break through the Gunners unforgiving defence, the chances began to dry up in the closing stages, though Welbeck did make an opportunity for himself as the game entered the final few minutes, but he put his effort from the edge of the area wide having picked the ball up on the byline.
It would be the Englishman's final act of a quiet return to the starting line up, as he was replaced by 18-year-old Eddie Nketiah moments later.
Ostersunds English substitute Jamie Hopcutt had a long range sight at goal in the final moments, and the Swedish side were then given the chance to get on the scoresheet when Bellerin brought down Tesfadelt Tekie inside the area, but Tom Pettersson's weak stoppage time penalty was easily held by Ospina.