In the other match, Kuwait swept aside Yemen 2-0 to join Iraq at the top of Group B.
Iraq opened the scoring in the 18th minute when striker Younis Mahmoud set up Salam Shakir. The match remained up for grabs into the second half but an own goal from Saudi Arabia's Osama Hawsawi in the 72nd settled the result.
In Kuwait's victory, Yousef al-Sulaiman scored in the 63rd and Bader al-Mutawa made it 2-0 in the 82nd.
The eight-team tournament is being held in Bahrain, which has faced anti-government protests for.
Iraq shocks Saudi Arabia 2-0 in Gulf Cup