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Lewandowski, who missed a penalty in Poland's opening draw with Mexico, was visibly emotional after pouncing on a mistake in the 82nd minute to double Poland's lead after Piotr Zielinski had given them a first-half lead.
After completing one of the tournament's greatest shocks when they beat Argentina 2-1, the Saudis, who failed to convert a first-half penalty, found Poland a tougher nut to crack at the Education City Stadium.
The win moved Poland to four points, one more than the Saudis, and left them needing a draw in their final game against Argentina on Wednesday to guarantee their spot in the knockouts.
The Saudis will head into their final match against Mexico with all still to play for.
The game sprang to life in the 39th minute when Poland shook themselves from their slumber to take the lead.
Matty Cash skipped down the right and crossed low for Lewandowski who lifted the ball over the keeper and pulled it back for Zielinski to fire into the roof of the net.
Their hopes of cruising through to halftime, however, were ended four minutes later when Krystian Bielik made minimal contact with the back of Saleh Al-Shehri's leg and he hit the turf.
The referee had initially waved away Saudi appeals but he was instructed to look at the VAR monitor and pointed to the spot, sparking celebrations from the Saudi players.
Those proved premature, however, as Salem Al-Dawsari's low effort was palmed away one-handed by Wojciech Szczesny, who was quickly on his feet to brilliantly parry the follow up from Mohammed Al-Breik over the bar.
Poland could have extended their lead in the second half when Arkadiusz Milik's header rattled the crossbar while Lewandowski hit the post with an effort that deflected off his knee.
Lewandowski, who had drawn a blank in his four previous World Cup games, did not have to wait too much longer for his goal.
Abdulelah Al-Malki slipped and Lewandowski pounced, sliding a tidy finish beyond Mohamed Al-Owais and into the net. The striker was seemingly in tears as he was greeted by team mates.
"Today everything I had inside, the dreams, the importance of the occasion, all those dreams from my childhood came through," Lewandowski said. "It was so significant."
Lewandowski's barren streak at the World Cup was somewhat puzzling. Now, in his fifth match at the tournament, it's over.
"I always wanted to score at the World Cup and this dream came true," he said. "It's not easy, because we didn't have many opportunities in the first match and I missed that penalty.
"The older I get, the more emotional I get. I'm aware that when it comes to the World Cup, that this might be my last World Cup. And I wanted to underline that I played at World Cups and I scored."
Saudi coach Herve Renard said he was proud of his players.
"No one around the world thought that we could play with this level. Yes, in Saudi Arabia, we know the players well, but they are unknown to the fans around the world.
"We are still alive. I'm proud of my players. We should have controlled the match better. If we scored the penalty kick, the first half would have ended in a 1-1 draw and then the match would have gone differently.
"It is easy to blame and shout at the players, I went to support Al-Malki after his mistake, and this is my way of coaching teams," Renard said.
