After South Korea's Cho Gue-sung equalized in second-half added time to cancel Abdullah Radif's opener, Sami Al-Najei and Abdulrahman Ghareeb had their penalties saved by Jo Hyeon-Woo to send South Korea through.
South Korea converted all their spot kicks to advance but they will have only two days to recover, however, with their quarter-final clash against 2015 champions Australia taking place on Friday.
"Asia is Green" read a banner alongside one with a player in a Saudi kit crouching with one hand on the Asian Cup trophy, as the vocal fans bouncing in the stands created an atmosphere that felt like a home game for Roberto Mancini's side.
Yet it was the South Korean team playing in bright orange that prevailed after the Gulf nation and three-time champions ran out of gas in the dying stages of the match and crumbled under the pressure.
Saudi Arabia had the best chance of the first half when two headers from a corner crashed off the crossbar while a third destined for the top corner was parried away by goalkeeper Jo.
At the other end, Son Heung-min was put through on goal twice but his tame efforts were easily saved as the half ended goalless.
However, Saudi Arabia took the lead immediately after the restart when halftime substitute Radif made an instant impact 30 seconds after coming on.
The lanky 21-year-old forward made a run in behind the defense to receive a pass from skipper Salem Al-Dawsari and beat the keeper with a shot that nestled in the far bottom corner of the net, before wheeling away in celebration.
The goal spurred the Saudis on and they made things difficult for South Korea who struggled to make inroads into the final third, until the final 10 minutes when they had a series of set pieces.
With Saudi Arabia having one foot in the quarter-finals, South Korea finally breached the Saudi defense in the ninth minute of added time when their pressure paid off and Cho headed home from close range to force extra time.
After failing to find a breakthrough in extra time, the arena was silenced when Jo made the two saves in the shootout.
Saudi fans began leaving in droves while Mancini also walked straight down the tunnel before Hwang Hee-chan stepped up and scored the decisive spot kick.