The Saudis played with ten men for over 10 minutes after midfielder Ahmed Ateef was sent off for a second bookable offense.
Saudi goalkeeper Walid Abdullah had an excellent game as he made a number of superb saves to keep the clean sheet.
Korea Republic, who already booked a place in South Africa, remain top of Group B with 15 points, while Saudi Arabia tie with North Korea on 11 points in second place.
The result means that Jose Peseiro's side will face a crunch finale with North Korea next week in Riyadh.
Both sides vie for the automatic qualification ticket to the World Cup, amid unfancied pressure from Iran.
Saudi Arabia must beat North Korea though as the latter are superior in the head-to-head record and goal difference.
Elsewhere in Group A, Australia maintained their unbeaten run with a 2-0 home win over Bahrain, while Qatar held Japan 1-1 at Saitama Stadium. Australia and Japan have already qualified.