Victory meant that Chris Wilder's team, who are eighth in the standings on 22 points, have avoided defeat in their opening eight away games of the campaign.
They last managed the feat in the top flight in the 1899-00 season, remaining unbeaten for 10 matches on the road.
Trailing 1-0 following a poor opening half at a wet and windy Carrow Road, the Blades equalised four minutes after the break when Stevens rose above Norwich's defence to powerfully head in fellow defender Baldock's cross from the right.
With Norwich still reeling, Baldock put the visitors ahead in the 52nd minute, twisting and turning before firing the ball past goalkeeper Tim Krul and into the bottom left corner after collecting a pass from John Lundstram.
Norwich midfielder Alexander Tettey had earlier marked his return to the starting lineup with the opening goal in the 27th minute, blasting a low shot past goalkeeper Dean Henderson after the Blades failed to clear Emiliano Buendia's corner.
Mario Vrancic could have doubled the Canaries' lead in the final seconds of the first half but the Bosnian midfielder's right-footed effort from distance was saved by Henderson diving to his left.
Blades defender Chris Basham was shown a red card 16 minutes from time for a poor challenge on midfielder Kenny McLean, but he was asked to return to the pitch after the Video Assistant Referee (VAR) deemed that his tackle deserved only a yellow.
The Blades survived a late scare when Norwich substitute Todd Cantwell wove his way past several defenders and got his shot away but Henderson was equal to the task, producing a sharp save to deny the English midfielder.
"We're an honest bunch and we don't need much telling, but there was a good reaction at halftime," Baldock told Sky Sports.
"We've come into the season full of belief and confidence. We got written off before a ball was kicked but we're doing ourselves proud."
Relegation-threatened Norwich, who remain 19th, travel to second-placed Leicester City next Saturday while the Blades host another promoted side in Aston Villa.