Petrounias added the Rio Games title to the world and European crowns he holds with a score of 16.000.
Zanetti lost out on the top prize by 0.234 of a point while Russia's Denis Abliazin had to settle for bronze.
Petrounias showed off his bulging muscles, and the Olympic rings tattooed on his upper back, as he smoothly moved from one difficult element to another.
There was not a wobble in sight as he held on to the Maltese cross - where a gymnast holds the rings with his body lined up horizontally - for what seemed an eternity before flowing into a number of handstands.
When he nailed the dismount, he saluted the crowd with a raised fist confident that he would become the first Greek since Dimosthenis Tampakos in 2004 to win the rings. It was Greece's second gold in Rio.
China's You Hao, silver medallist behind Petrounias at last year's world championships, had been expected to push him all the way with a routine that had the highest 7.000 difficulty score.
However, when he almost stumbled off the mat from his double twisting-double layout somersault dismount, his medal hopes were dashed and he finished sixth out of the eight finalists.
Yuri van Gelder, the 2005 world champion, had qualified for the final but was a no show after he was expelled from the Olympics for violating Dutch team rules on alcohol consumption following the qualifying competition last weekend.