Goals from Robert Lewandowski and Piotr Zielinski denied Saudi Arabia a second World Cup upset in as many games, as Poland took the points with a 2-0 win in Al Rayyan.
Lewandowski set up Zielinski to fire Poland into a 40th-minute lead at the Education City Stadium before the Polish captain added a goal to go with his assist in the final 10 minutes.
Herve Renard's Saudi Arabia had the chance to level the scoreline in first-half stoppage time but Al Dawsari was denied by Wojciech Szczesny.
Three points for Poland sees them go top of Group C, ahead of Argentina vs Mexico and overcome a disappointing display in their first game.
As for the Green Falcons, the loss in Al Rayyan knocks them back to Earth, after the heady heights of the win over Argentina in the first round of games, and knocks them off top spot in Group C.
Story of the match
Saudi Arabia started the better team and could have gone ahead after 10 minutes, when Mohamed Kanno drilled a shot high towards goal, forcing a smart stop from Szczesny.
But it would be Poland who hit the front first.
Matty Cash's cross from the right-hand side was kept alive in the area by Lewandowski, who teed up Zielinski to rifle a shot into the roof of the net and give Poland a crucial lead.
The Green Falcons would have the perfect opportunity to draw level in first-half stoppage time.
Krystian Bielik fouled Saleh Al Shehri in the area, giving last round's match-winner Al Dawsari the chance to level the scores from 12 yards but the Polish shot-stopper got down to his right to save the penalty and keep the scoreline at 1-0.
The Saudis continued to push and Al Dawsari was at the centre of it again.
His run into the area caused a scramble just yards from goal and it would fall for him again at the end of it, but his effort towards goal was blocked and Poland eventually cleared.
Al Dawsari was at the heart of everything positive about the Green Falcons' second-half performance and he almost set up an equaliser.
A clever turn allowed him to slip in Firas Al Buraikan but he could only fire wide from a tight angle, giving Poland another let-off.
Despite the Saudi pressure, though, it was the Polish who almost doubled their advantage against the run of play.
Przemyslaw Frankowski's delivery from the left-hand side was met in the middle by Arkadiusz Milik with a diving header but his effort cannoned back off the crossbar.
Moments later the Saudi woodwork was struck for a second time, when a low cross from the right was met by Lewandowski at the front post but his flick towards goal came back off the post.
Saudi Arabia continued to push through, with Saud Abdulhamid's cross falling to Al Dawasari on the edge of the area but he dragged his shot wide of the right-hand post.
Despite all of the Green Falcons' best efforts, it would be Poland who sealed the points ten minutes from time.
Poor play from the back allowed Lewandowski to latch onto a loose ball and slot past Mohammed Al Owais to score his first-ever World Cup goal and round off a crucial win for his side.
Player of the match
Robert Lewandowski
Among a handful of standout performers, whether it be Szczesny for his penalty save, Zielinski for his opener, or Al Dawasari for causing untold amount of problems for the Polish defence, Barcelona forward and Poland's captain Lewandowski took the acclaim.
After keeping the chance alive to set up Zielinski for Poland's first, he was unlucky not to get on the scoresheet earlier in the second half, after he struck the post.
However, he capitalised on a Saudi defensive mess to finally score his first World Cup goal for his country at the age of 34.
A constant threat all game, even when Poland were under pressure for large parts of the second half, Lewandowski earned a match rating of 8.9 on WhoScored for his efforts at the Education City Stadium.
Lineups
Poland XI: Szczensny (GK), Cash, Glik, Kiwior, Bereszynski, Krychowiak, Bielik, Milik, Zielinski, Frankowski, Lewandowski
Saudi Arabia XI: Al Owais (GK), Abdulhamid, Al Amri, Al Boleahi, Al Breik, Al Malki, Al Najei, Kanno, Al Buraikan, Al Shehri, Al Dawasri