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.
After initially backing up Russell, Sainz had to pick up the pace after both Russell and Hamilton pitted under a virtual safety car when Esteban Ocon's Alpine expired.
The Mercedes pair enjoyed a clear pace advantage in the closing stages, but Russell was unable to move ahead of Norris before crashing on the final tour to elevate Hamilton into third.
"I knew it was going to be a long stint on hard," Sainz said.
"I had to keep George, I had to keep him slowing down to don't give him a safety car or a medium tyre opportunity, and it worked to perfection.
"It was just quite tight at the end, but we gave Lando a bit of DRS to help him and then in the end, we made it to P1."
