The hosts finished as runners-up last time round but went one better in front of their own fans after 120 minutes finished goalless.
The win by Claude Le Roy’s men means that the nation hosting the last three Gulf Cups has lifted the trophy.
It was a dramatic finish as the teams successfully converted their first five penalties at Sultan Qaboos Complex Stadium.
Saudi Arabian midfielder Taisir Al Jassim was the first to miss and Mohamed Rabih kept his nerve to fire home and clinch the win.
Oman had the better of the chances in the game itself, however. Ismail Al Ajmi hit the bar at the end of the first half, and they hit the woodwork once again late in the game.
Saudi Arabia had their chances but couldn’t find a way past Oman’s goalkeeper, Ali Al Habsi.