The Spaniard led all 62 laps under the lights at the Marina Bay track, producing an inch-perfect tactical drive to convert pole position into his second F1 win by 0.812s.
On aged hard tyres, Sainz kept fellow one-stopper Norris at bay in the closing laps as George Russell and Lewis Hamilton closed them down with fresher medium tyres on their Mercedes to form a four-car train.
But despite the intense pressure, Sainz said he was confident he had enough in hand to score Ferrari's first win since Austria in July 2022.
After hailing a "perfect" execution from his Ferrari team, Sainz remarked: "I felt under control, to be honest. I always felt like I had the headspace and the pace in hand to do whatever I wanted to do.
"I'm not gonna lie, you're under pressure and you obviously are very close to making any kind of mistake, but I felt under control.
"I felt like I could manage well, and we brought it home. That was the best feeling you know. I am over the moon right now."
Sainz explained that the safety car called after Logan Sargeant understeered into the Turn 8 wall on lap 19 had made life more difficult for him as he had to extend his second stint.
Source: Autosport