The group stage of the 2015/16 UEFA Champions League was completed on Wednesday night with the Round of 16 combatants now sorted.
The Frenchman headed home Aaron Ramsey's cross in the 29th minute before producing a quality finish from Joel Campbell's reverse pass four minutes into the second half.
The treble was complete with just over 20 minutes remaining when he coolly converted from the penalty spot to send Arsene Wenger's men through to the knockout stages of Europe's elite club competition for the 16th straight season.
Lionel Messi opened the scoring for the Catalan club when he rounded Bayer keeper Bernd Leno after a defence-splitting pass from Ivan Rakitic before Javier Hernandez notched his 12th goal in his past 11 outings when firing home just three minutes later.
Barcelona remained top of the group and will be joined by AS Roma in the next phase after the Italians drew 0-0 with BATE Borisov, allowing them to finish ahead of Bayer following the 3-2 result to the Giallorossi in early November.
The Blues finished two points ahead of Dynamo Kyiv who defeated Maccabi Tel Aviv 1-0 to bypass Porto on their way to the last 16.
And Group H had Gent become the first Belgian club in 15 years to reach the knockout stages thanks to their 2-1 win over group winners Zenit Saint Petersburg as Valencia slumped to a 2-0 home defeat to Lyon in Gary Neville's first game as manager.
2015/16 UEFA CHAMPIONS LEAGUE - GROUP STAGE SCORES
AS Roma (ITA): 0
BATE Borisov (BLR): 0
Stadio Olimpico, Rome, Italy - 29,489
Dynamo Kyiv (UKR): 1 (Denys Harmash 16')
Maccabi Tel Aviv (ISR): 0
Olympic Stadium, Kiev, Ukraine - 475