The Gunners survived a huge scare as Ostersunds FK came within a goal of levelling their tie at the Emirates Stadium thanks to two quickfire strikes in the first half.
Atletico Madrid took the lead on seven minutes in their second leg at home to Copenhagen through Kevin Gameiro for a 5-1 win on aggregate, while Dortmund left it late to salvage a 1-1 draw at Atalanta BC for a 4-3 win in the tie.
Napoli came within a whisker of progressing against RB Leipzig at the Red Bull Arena but goals from Piotr Zielinski and Lorenzo Insigne were not enough to overturn a 3-1 first-leg deficit as the Germans won on away goals.
Also through to the next round are Sporting Lisbon, Viktoria Plzen, Lyon, Red Bull Salzburg, AC Milan and Marseille, while Astana, Partizan Belgrade, Villarreal, Real Sociedad, Ludogorets Razgrad and Braga are out of the competition.
Results in full: Lokomotiv Moscow 1-0 Nice, Atletico Madrid 1-0 Copenhagen, Dynamo Kiev 0-0 AEK Athens, Lazio 5-1 Steaua Bucuresti, Viktoria Plzen 2-0 Partizan, RB Leipzig 0-2 Napoli, Sporting Lisbon 3-3 Astana, Villarreal 0-1 Lyon, Zenit St Petersburg 3-0 Celtic, AC Milan 1-0 Ludogorets Razgrad, Arsenal 1-2 Ostersunds, Atalanta BC 1-1 Borussia Dortmund, Athletic Bilbao 1-2 Spartak Moscow, Braga 1-0 Marseille, Red Bull Salzburg 2-1 Real Sociedad