Story of the match
Norwich were on the front foot early, pressuring the Rotherham defense early, Marko Vrancic going just wide with a low drive inside of four minutes.
He would nearly get the Canaries on the board moments later, combining with Emiliano Buendia to set up Pukki, but his shot was easily handled by Viktor Johansson.
The chances kept coming as Pukki turned provider, playing the ball inside on the left to Vrancic, who again went wide. Rotherham then thought they had taken the lead through Clark Robertson, only to see the goal ruled out for offsides.
Soon after, Norwich were ahead. Buendia diverted a lovely pass, Todd Cantwell dummied and Pukki slotted past Johansson for his 15th of the campaign, giving the Canaries a 1-0 lead.
Rotherham's pressing style forced the hosts to work hard for their chances, but six minutes before halftime, Vrancic squared for Buendia, who saw his effort blocked by the Millers defense.
The Millers were unlucky not to have levelled after the halftime break, Max Aarons only heading a corner clear as far as Ben Wiles, whose half-volley on the edge of the area hit the post.
Buendia then played a delightful pass on the left to the edge of the area to Cantwell, but he could only screw his shot wide. Kenny McLean met Buendia's corner, but Carl Ihiekwe cleared off the line.
More chances for Norwich as McLean lofted the ball over the Rotherham defense on 70 minutes, Pukki clear, but he shot straight at Johansson. That miss almost proved costly.
Substitute Freddie Ladapo drove into the area, cutting back to Matt Crooks, who saw his shot, destined for goal, blocked by Aarons. On 82 minutes, Cantwell lofted a pass from Pukki, but he again went wide.
There would be no more chances as Norwich saw out the victory, the Canaries destined for a return to the Premier League while Rotherham fight for the Championship lives.
Man of the match: Emiliano Buendia
While it was Pukki who scored the goal, the Argentine was at the heart of every chance that Norwich created. His passes cut open the Rotherham defense, often finding Vrancic or Pukki on the edge of or inside the Millers area.
Norwich showed why they're at the top of the table
Playing, attacking, free-flowing football, the trio of Pukki, Buendia and Vrancic set the tone with a number of chances, often in excellent positions, putting the Rotherham defense under constant pressure. No other team consistently puts out performances like this and that's why they'll be playing in the top flight next season.
Rotherham will be disappointed not to have come away with a point
Despite Norwich creating more chances, the visitors did have their fair share of opportunities. Lewis Wing, Robertson and Crooks all could have scored, but for various reasons, they were kept out. Should they play like this against lesser competition, Paul Warne's side will give themselves every chance of staying up.