The Gunners opened the scoring just over half an hour in through Pierre-Emerick Aubameyang's clinical finish from their first serious effort of the night.
Danny Welbeck doubled his side's tally early in the second half, which Aubameyang and Mesut Ozil added to, but the visiting side staged a mini comeback as Volodymyr Chesnakov and Vyacheslav Sharpar pulled back late goals.
Relive how the 90 minutes of action unfolded with Sports Mole's live text coverage below.
STARTING XI: Leno; Lichtsteiner, Sokratis, Holding, Monreal; Elneny, Torreira; Welbeck, Mkhitaryan, Iwobi; Aubameyang
SUBS: Martinez, Bellerin, Lacazette, Ozil, Guendouzi, Nketiah, Smith Rowe
STARTING XI: Shust; Perduta, Chesnakov, Dallku, Artur; Kobakhidze, Sharpar, Kravchenko, Rebenok; Kolomoets; Kulach
SUBS: Tkachenko, Girogadze, Sakiv, Misik, Sklyar, Careca, Sergiychuk
Unai Emery: "The Premier League is the first competition because it's giving us a big responsibility. Other competitions are very important too. Today, we are only thinking about giving our supporters the first performance and a good 90 minutes on the pitch at the Emirates. Every title for us is very important. In my career, the ambition is very important for continuing to improve and continuing to achieve the objectives in my career personally and with the team. I want to play for every title going forward."
Vasyl Sachko: "We have a planned stroll for the team. We are not here as tourists, we are here to play, but we will have a walk around tomorrow as part of our warm-up. I have never been here as a fan, I haven't been here once but the impressions are the best they could be. Our club is writing history, writing history for our city and that is a huge honour for us. Our objective is to get the players to understand this. Our team is playing against Arsenal, we understand we are a modest club. We don't have any stars in our team."
ARSENAL SUBS: Martinez, Bellerin, Lacazette, Ozil, Guendouzi, Nketiah, Smith Rowe
VORSKLA POLTAVA SUBS: Tkachenko, Girogadze, Sakiv, Misik, Sklyar, Careca, Sergiychuk