DUBAI—The prospect of Iranian oil flooding an already oversupplied crude market sent Saudi Arabian stocks sharply lower Sunday, while the end of economic and financial sanctions lifted Iranian equities.

Saudi Arabia’s benchmark Tadawul All Share Index tumbled 5.4% to 5520.41, leading an Arab Gulf markets rout as oil prices settled below $30 a barrel for the first time in 12 years amid worries that a global glut will continue as Iran increases its crude exports. Tehran Stock Exchange’s main TEDPIX index rose 0.9%, according...