The 31-year-old settled what looked likely to be a goalless draw for large parts with an overhead kick into the top corner of the net five minutes from time at the Rajko Mitic Stadium.
Giroud, who scored a similarly impressive goal against Crystal Palace on New Year's Day, insists that he was initially hoping to find a better-positioned teammate inside the crowded box, but with a lack of options instead took on the shot himself and beat Milan Borjan with a fine finish.
"In that position, I can control the ball and try to play with another teammate," he told reporters. "But I didn't see anyone so I tried to take it as I can, a little bit like against Palace, I've been a bit lucky because it's top corner and it's the back of the net.
"It's nice for the team, I'm happy for the team because we've been resilient until the end and we keep believing in our game and we knew it was going to be a tough game and just needed to be patient and play our game with our qualities.
"It has been very difficult because it's an amazing atmosphere here, special atmosphere, the crowd is behind their team and it was a tough game but we're very pleased with the three points."
France international Giroud now has three goals in 11 outings for Arsenal in all competitions this season.