The Gunners left-back did did well to get his head over a bouncing ball before expertly firing into the corner of the net from the edge of the box on 17 minutes.
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That proved to be the only goal of the Emirates Stadium clash, which saw Arsenal miss a number of chances to extend their lead with Fabio Vieira and Eddie Nketiah going close.
But the Swiss outfit were a threat throughout and had plenty of chances of their own with Aaron Ramsdale doing well to deny a Jonathan Okita header in the first half.
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After the break Adria Guerrero had a goal disallowed for a marginal offside, while Bohdan Viunnyk's left-footed effort whistled just past the post.
There was also quite a comical moment earlier in the second half as match-winner Tierney lost a large chunk of his shirt after being pulled back by Nikola Boranijasevic.
With PSV Eindhoven winning 2-1 at Bodo/Glimt, Arsenal needed to get the three points to secure their place in the last-16.
They managed exactly that and will avoid the play-off round and a potential tie against the likes of Ajax, Barcelona and Juventus, who drop down to the Europa League after coming third in their Champions League groups.
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Manchester United will be in the Europa League play-off as their 1-0 win at Real Sociedad wasn't enough to see them top of their group.