The match appeared to be heading towards a goalless draw until Giroud directed an effort into the top corner from eight yards to earn the Gunners their third successive win in Group H.
Red Star had their own chances but after Milan Rodic was sent off for two bookable offences, the home side were unable to hang on for what would have been a credible point.
Arsene Wenger made a total of nine changes to his Arsenal starting lineup and it took time for his players to settle in the hostile environment at the Red Star Arena.
Just before the half-hour mark, the Ghanaian forward met a corner with his head, but his effort was directed into the ground with the ball bouncing up to hit the woodwork.
Both teams needed an improvement after the restart and five minutes into the second half, Reiss Nelson battled through a tackle to engineer a chance for himself, but the youngster's strike was too close to Borjan at the near post.
It did not take long for Red Star to respond, with Krsticic meeting an outswinging cross from the right to force Cech into a solid save from 12 yards out.
The game continued to be end to end and Mohamed Elneny gifted Slavoljub Srnic the chance to shoot on goal from inside the penalty area after a stray back-pass, but Cech was on hand to tip his attempt over the bar.
From the hour mark onwards, chances dried up at both ends with both teams seemingly content with a point, but with 10 minutes left, Arsenal received a boost when Rodic was sent off for a second yellow card.
Five minutes later, Giroud got himself on the scoresheet with another sensational strike. The forward had done nothing all match but the Frenchman was able to send an overhead kick into the top corner after a fine interchange which also involved Jack Wilshere and Walcott.
Red Star pushed for an equaliser but Arsenal remained in control to stay at the top of the group, now with a five-point advantage after beating their nearest rivals.