The Chilean forward, acquired last month from Barcelona for 35 million pounds (then $60 million), scored in first-half injury time to put Arsenal ahead following a 0-0 first leg last week in the home-and-home, total-goals series.
Arsenal finished a man short after defender Mathieu Debuchy was ejected in the 75th minute for his second yellow card, given for a foul om Mustafa Pektemek.
The Gunners have been in the group stage every season since 1998-99, and Athletic Bilbao is back for the first time since then after beating Napoli 3-1 to advance on 4-2 aggregate.
Malmo will be Sweden's first group stage representative in 14 years after beating Salzburg 3-0 to advance 4-2. Bayer Leverkusen routed Copenhagen 4-0 for a 7-2 win.
The draw is Thursday.