The Gulf nation, a West Asian powerhouse and three-time winners of the tournament, made a bad start in Australia when they lost their opening match 1-0 to China in Brisbane on Saturday.
Their hopes of advancing to the quarter-finals looked to be in danger of suffering another blow when they fell behind against North Korea at AAMI Park on Wednesday, but Naif Hazazi's leveller, a Mohammad Al Sahlawi brace and Nawaf Al Abid's late goal saw them respond well to secure an important three points.
Al Abid's strike came from the penalty spot after Lee Yon-jick had been dismissed for handling a shot that bounced off the crossbar.
North Korea, who failed to impress in their opening 1-0 loss to Uzbekistan, at first looked unrecognisable from the side well beaten in Sydney on Saturday, making a flying start to the match and deservedly opening the scoring after 11 minutes.
A long ball forward was headed down for Pak Kwang-ryong to unleash a strike at goal. Saudi goalkeeper Waleed Abdullah could only parry the vicious effort and Ryang Yong-gi gratefully tucked away the rebound to net his country's first Asian Cup goal since 1992.
With North Korea content to sit back and defend the lead, Saudi Arabia initially did little to suggest they were capable of getting back into the match.
That changed on 38 minutes, when a turnover in midfield saw Cosmin Olaroiu's men spring on the counter-attack. The move ended with Al Abid slipping in Hazazi to equalise, the Al-Shabab forward making amends for his penalty miss in the loss to China.
The Saudis will feel they should have gone in 2-1 up at the break, only a brilliant reflex save from Ri Myong-guk denying Al Abid in the 42nd minute. The Al-Hilal man did well to control the ball with his chest and unleash a volley on the turn, but Ri got down low to his left and tipped the firm strike around the post.
Saudi Arabia started the second half strongly, Al Sahlawi heading just over the bar in the 50th minute.
Two minutes later the Al-Nassr forward had another chance and this time he couldn't miss, guiding home Abdullah Al Zoari's cutback after a neat exchange of passes inside the penalty area.
North Korea were clearly rattled and things quickly went from bad to worse for Jo Tong-sop's men. Barely another two minutes went by before another error let in the Saudis again.
Jang Song-hyok tried to clear but succeeded only in smashing the ball into the chest of Al Sahlawi, who was left with a simple finish into an unguarded net to make it 3-1.
Salem Al Dawsari almost scored the goal of the tournament so far in the 76th minute, advancing into the area, reaching the byline and then beating two men before lobbing the goalkeeper.
The ball hit the bar and then struck the arm of Lee, who was duly dismissed. Al Abid's spot-kick hit one post and then the other, but he got there first to hook the ball home before Ri could get across and clear it.
Even before the fourth goal went in, there never looked like being any way back for toothless North Korea, who take on China in Brisbane on Sunday with their elimination from the competition already confirmed.
The Saudis will face Uzbekistan on the same day in Melbourne, with a quarter-final against the Group A winners or runners-up, Australia or South Korea, the prize on offer.
