The 23-year-old made several solid stops in the first half as he looked to maintain his clean sheet.
The stopper has to be alert early on to race out and clear as Richmond Boakye looked to race through but his finest contribution came with 36 minutes on the clock.
Red Star caught Arsenal cold with a quickly-taken corner and when a shot from range was deflected up into the air it dropped to Savic, who headed for goal, only to be denied by a fine finger-tip save from Macey.
The stop sent Arsenal fans into raptures on social media, with some jokingly suggesting that he had now offered more than veteran Petr Cech this season.
Check out the save for yourself below:
Brilliant save by Matt Macey pic.twitter.com/XVr8IkI5iO
— Terje (@ArsenalTerje) 2 November 2017