Defender Andriy Rusol opened the score for Ukraine in the 4th minute before a powerful Serhiy Rebrov strike in the 36th minute doubled the lead.
Captain Andriy Shevchenko added the third only seconds after restart while Maxim Kalinichenko sealed the win with an 84th minute goal.
The win put Ukraine at level with Spain at the summit of Group H on three points while Saudi Arabia lie in third place with a single point.
Spain will take on Tunisia later on Monday in a bid to extend their points tally.
The win is Ukraine's first in the history of the World Cup after the East Europeans lost 4-0 to Spain on debut last week.
The Ukrainians made clear of their intentions when they notched the first goal as early as the first minute.
Rusol kneed home the first between Saudi keeper Mabrouk Zayed's legs from a Kalinichenko corner-kick.
The hapless Zayed was victimized once more when he slipped while trying to stop Rebrov's screaming shot in the 36th minute as Ukraine extended their lead.
Thirty seconds after re-start, Shevchenko towered to headed home the third from another Kalinichenko set-piece.
The Saudis conceded the fourth goal when Shevchenko raced down the left flank and squared to the onrushing Kalinichenko who drilled the ball home to seal the win.