The Gunners recovered from a slow start with a ruthless display in the second half, getting the job done through a couple of goals from Pierre-Emerick Aubameyang and one apiece for Danny Welbeck and Mesut Ozil.
Three-time winner of the competition Emery once again saw his side fail to keep a clean sheet, however, as Volodymyr Chesnakov and Vyacheslav Sharpar bagged consolation goals for the Green-Whites in what is their second ever appearance in a major European competition.
Vorskla, third-placed finishers in Ukraine last season, had scored just three goals in their last seven competitive away outings and were more than happy to sit deep for large parts here.
The home side were not exactly taking advantage of their high possession count, though, as they became a little too reliant on full debutant Lucas Torreira to create openings from his deep starting position.
Alex Iwobi's wayward shot 29 minutes in was their only attempt of any note in the opening half-hour, in fact, as an Arsenal side showing eight changes from their most recent outing struggled to get going.
The breakthrough moment would arrive shortly after, however, and it all came from a rare Vorskla voyage forward into the opposition half.
That goal made Aubameyang the first Arsenal player to score more than once in all competitions this season, but the Gunners did not exactly build on the lead.
Not until the final minute of the half did they register their next attempts, with Aubameyang grazing the post with his long-range curler and Mkhitaryan being denied by Shust from inside the area.
Arsenal managed to push on from that strong finish to the first half, taking just a few minutes of the second period to double their tally for the night.
A clipped Mkhitaryan cross from the left was guided past Shust by the head of Welbeck, giving last season's beaten semi-finalists some breathing space and a chance to flex their muscles.
Welbeck could have had a second 90 seconds later, only to send Aubameyang's pass wide of the post when under pressure, and the Gabonese striker volleyed over the bar from a glorious position moments later.
Arsenal did not have to wait long for the killer third to arrive, though, with Aubameyang this time picking out the bottom corner after pouncing on his own misplaced pass just outside the opposition box.
Mkhitaryan miscued his shot as Arsenal, without a home defeat on matchday one in European competition since 2003, closed in on a fourth goal.
The next 20 minutes saw the Green-Whites venture forward more regularly in search of a consolation, but Arsenal were always the more likely to bag the game's next goal and it duly arrived before full time.
Stephan Lichtsteiner lifted the ball over Shust towards the back post, where substitute Ozil was waiting to help it past a couple of defenders on the line with the underside of his boot.
Arsenal could not keep the opposition out, however, as Chesnakov thumped the ball past debutant Bernd Leno after the hosts failed to clear their lines from a corner.
Sharpar then pulled back a second for Vasyl Sachko's men from the final kick of the match, sending the ball high into Leno's net from right on the edge of the area with an equally-as-emphatic finish.
ARSENAL (4-2-3-1): Leno; Lichtsteiner, Sokratis, Holding, Monreal; Elneny, Torreira (Guendouzi 57'); Welbeck, Mkhitaryan, Iwobi (Smith Rowe 70'); Aubameyang (Ozil 57')
VORSKLA POLTAVA (4-4-1-1): Shust; Perduta, Chesnakov, Dallku, Artur; Kobakhidze (Sergiychuk 77'), Sharpar, Kravchenko (Sklyar 70'), Rebenok; Kolomoets; Kulach (Careca 75')