Arsenal finished top of Champions League Group A thanks to a Lucas Perez hat-trick in Basel and Paris St-Germain's draw with Ludogorets Razgrad.
PSG would have sealed top spot with victory, with anything less allowing in the Gunners, who took control through two Perez tap-ins.
Perez drove in his third from the edge of the box and Alex Iwobi rolled in a fourth before Seydou Doumbia cut through for a Basel consolation.
A 2-2 draw in Paris left Arsenal top of a group for the first time since 2011-12.
Arsene Wenger's side failed to make it past the last 16 that year, and have fallen at the first knockout stage in each of the past six seasons.
Aside from breaking their run of second-placed group finishes, the Gunners have also gone through a group stage unbeaten for the first time since they reached the final in 2005-06.
Gunners' good fortune?
A 2-2 draw at home against PSG in November looked to have consigned Arsenal to second place and, in theory, a harder assignment in the last 16.
Their only hope of topping the group was help from Bulgarians Ludogorets, who twice led in Paris and, despite Angel di Maria's late equaliser, held on to seal a place in the Europa League.
As a result, Arsenal know they will avoid Barcelona and Monaco, who have knocked them out in the past two seasons respectively, as well as Atletico Madrid and Napoli in Monday's draw.
However, they will face one of:
Bayern Munich, their conquerors in 2013 and 2014
One of Borussia Dortmund or Real Madrid
Benfica
Bayer Leverkusen
One of Porto or FC Copenhagen
One of Juventus, Seville or Lyon
Spaniard Perez has struggled to make an impression since a £17m move from Deportivo La Coruna in August, making just one Premier League start and only finding the net with a double against Nottingham Forest in the League Cup.
Here he was twice in the right place at the right time, an empty net at his mercy first after Kieran Gibbs rolled the ball across goal, then when a Gibbs shot was parried, both strikes coming at the end of flowing passing moves.
Perez completed his hat-trick soon after half-time, surging towards the Basel goal and angling a finish past a weak attempt at a save from home goalkeeper Tomas Vaclik.
Arsenal were incisive and consistently dangerous on a freezing and misty night in Switzerland, with Alexis Sanchez and Mesut Ozil constantly linking - Sanchez's delightful pass finding Ozil, who fed Iwobi from the left for the fourth.
Gibbs grabs his chance
Gibbs is another Arsenal player who has been short of opportunities this season, making only one start in the Premier League.
The England left-back was brilliant in Basel, not only having a hand in Perez's first two goals, but also winning the ball and playing a through pass for the third.
As Gibbs often took an advanced position, Basel did find some joy down the Arsenal right, with Renato Steffen cutting in to force a save from David Ospina and Matias Delgado heading over from inside the six-yard box.
The visitors' defence, including Rob Holding, was occasionally ragged, and when Holding lost out to Seydou Doumbia, the Ivorian wonderfully turned Laurent Koscielny for a consolation that Basel deserved.
'You feel a bit less guilty'
Arsenal manager Arsene Wenger: "I thought Ludugorets were a good side - they made a great result that helps us top the group, which was what we wanted.
"We did the job in a convincing way, we were mobile and overall had a committed performance.
"It is difficult to know but you feel a bit less guilty if you have a bad draw [after finishing] first rather than second - we have done our job and let's see what happens.
"I think Perez took advantage of the fact we created good chances - he is a goalscorer you know. He has shown tonight he has a good smell for the goal."
What's next?
Arsenal will be seeded for Monday's last-16 draw, but before then host Stoke City in the Premier League on Saturdat. Basel go out of Europe, without even a place in the Europa League, but can console themselves with a 12-point lead in the Swiss top flight.
(BBC)
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