After wasting a few promising first-half opportunities, the best of which saw Francis Coquelin hit the post, the Gunners were made to pay by their out-of-form opponents.
Guirassy stepped up after being brought down by Mathieu Debuchy inside the box to blast home the spot kick, keeping his side in last-32 contention in the process.
Relive how the 90 minutes of action unfolded with Sports Mole's live text coverage below.
STARTING XI: Ospina; Chambers, Mertesacker, Holding; Debuchy, Coquelin, Elneny, Maitland-Niles; Wilshere, Welbeck, Giroud
SUBS: Macey, Sheaf, Willock, Iwobi, Nelson, Akpom, Nketiah
STARTING XI: T.Horn, Sorensen, Maroh, Mere, Klunter, Ozcan, Jojic, J.Horn, Cordoba, Guirassy, Osako
SUBS: Kessler, Olkowski, Risa, Lehmann, Rausch, Nartey, Bisseck
The reverse fixture in September marked the first time that these two sides have faced off in European competition; Arsenal recording a 3-1 victory in North London after recovering from Jhon Cordoba's superb early strike. The Gunners' record against German opposition reads 17 won, six drawn and 14 lost in 37 matches, with eight of those defeats coming away from home.
Three-times Premier League champions Arsenal have not lost any of their last nine UEFA Cup/ Europa League matches, excluding penalties, since a 2-1 defeat to Deportivo La Coruna in the 1999-00 campaign. The Gunners have won all four away matches since that slender loss in Galicia 18 years ago.
Peter Stoger: "The players that we have in their respective positions will pretty much have to take on both matches completely. We do not have a large selection right now. It is certainly a large challenge, but we want to use the opportunity we have to remain in this competition. We are still in it."
Arsene Wenger: "[Welbeck] has the potential to go and if he's fit he will go, I'm convinced of that. It is a big year for him, but I want it to be a big year for him and for Arsenal too. As a consequence of that, the best way to go to the World Cup is not to think 'I have to prepare for the World Cup', it is to do well for your club and automatically you are in the national team."
The home side have already been forced into making one change, bringing on Rausch for Maroah. Arsenal have a full selection of back-ups to choose from, meanwhile, with talented youngsters Nketiah, Nelson and Willock among them.
FC KOLN SUBS: Kessler, Olkowski, Risa, Lehmann, Nartey, Bisseck
ARSENAL SUBS: Macey, Sheaf, Willock, Iwobi, Nelson, Akpom, Nketiah