The incident took place in the 16th over from Spencer Johnson when he dug in a short ball and Sherfane Rutherford hooked it over fine leg for half-a-dozen.
As the ball sailed into the first tier, the spectator casually put his right hand out and grabbed the ball effortlessly while holding a coffee cup in his other hand.
Amid a huge cheer from the fans, the commentators too were mighty impressed with the catch as the spectator pulled it off without spilling a drop of his drink.
Riding on Rutherford (67 not out) and Andre Russell (71) blitz, West Indies amassed 220 for 6 after opting to bat.
Australia have already pocketed the three-match series after winning the Hobart and Adelaide T20Is.