Prior to this encounter the two sides had met only once in their history, way back in 1978/79 when Red Star were victorious over two legs and but it was the visitors who claimed the points on this occasion.
The game started at a slow tempo as both sides went about getting a feel for each other.
The first real chance came after 15 minutes and it dropped to Theo Walcott, who went into the game having scored six goals in his last eight European games. Jack Wilshere clipped in a free kick and when the hosts failed to clear Rob Holding prodded it into the path of Walcott, but he could only fire straight at Borjan from 12 yards with his left foot.
Far from go into their shells at this stage, the hosts started to establish themselves and looked dangerous on the counter with Richmond Boakye, reportedly a target for the likes of Chelsea, working the channels impressively and creating space for his team-mates.
The hosts were the next to threaten as Boakye rose highest to meet a corner from the right and guide a downward header into the turf and back off the bar.
The former champions of Europe went close again five minutes later as Srnic did well down the right before crossing to the back post, Nelson couldn’t quite get there but it was perfect for Radonjic and he teed himself up before firing a fierce effort towards the near post, only to see it palmed away by Cech before Nelson recovered to block the rebound to safety.
Arsenal continued to dominate the ball for the rest of the first 45, with the Serbians happy to sit in and play on the counter and the ‘Gunners’ were unable to find a way through, meaning that the two sides went into the break level.
The second half started at a much higher tempo as Arsenal started to run at the hosts, who struggled to deal with the more direct approach.
Reiss Nelson grew into the game more, first a direct run lead to a half-chance for Olivier Giroud, but he could only screw Walcott’s effort up into the air and into the hands of Borjan as he looked to divert it on target.
The youngster did call the home goalkeeper into a save just minutes later as he found a yard of space and struck a powerful effort towards the near post but Borjan was equal to it.
Not to be outdone, Red Star were next to threaten, first Kristicic headed straight at Cech from 12 yards after meeting Stojkovic's cross from the right, before Srnic pounced on a momentary lapse from Elneny and forced Cech to palm a powerful effort away for a corner.
Arsenal controlled the play for the majority of the second half as the hosts dug in a seemingly looked to settle for a point.
The hosts were reduced to ten men with ten minutes to go as Rodic was harshly given a second yellow after he was adjudged to have caugh Coquelin with a trailing arm when challenging for a header.
Arsene Wenger's men took full advantage of their opponents' misfortune as they scored the winner with the one real piece of quality in the entire game.
Wilshere and Walcott played a nice one-two on the edge of the Red Star box before the latter headed the ball down to Giroud, who turned the ball home via an acrobatic overhead kick from eight yards.
It was a goal worthy of winning any game and it puts Arsenal in control of their Group with three wins from three so far ahead of the return fixture in two weeks' time.