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 earl in the first half.
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At the Emirates, Arsenal missed 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 goalkeeper 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.
"It's been coming - I've not scored in a while!" the defender said afterwards.
"I've been getting closer in the last few games and I'd just like to tell the boys it's about time I scored.
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"Job done is how you'd describe it," he added. "We'd have liked it to be more comfortable but it was never going to be easy. They came here with a lot to play for as well. But we dug deep and we defended well at the end. They put a lot of pressure on us."
With PSV Eindhoven winning 2-1 at Bodo/Glimt, Arsenal needed to get the three points to secure their place in the last-16.
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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.
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.