Despite dominating the match for long periods Norwich could find no way through a determined rearguard, with the visitors picking up another useful point in their battle against the drop.
Buoyed by their excellent 2-0 win at Blackburn on Good Friday, Norwich completely dominated the opening stages, with Josh Vickers making two excellent stops in the first five minutes to deny first Gabriel Sara and then Josh Sargent.
The pressure on the Rotherham goal was incessant and Teemu Pukki wasted a good chance to open the scoring when he dwelt on the ball too long after being put clear by a ball from deep, allowing Cohen Bramall to intercept.
Pukki, who recently announced he would be leaving the Canaries at the end of season, then fired inches over and Sam McCallum's piledriver was deflected just wide as the one-sided nature of proceedings continued throughout the first half.
The Millers rarely threatened, although they fluffed a decent opportunity midway through the half when Tariq Fosu mis-kicked after being picked out in space by Jamie Lindsay.
It was a similar story after the interval, with Norwich on the front foot and their opponents largely content to sit back and soak up the pressure.
The visitors had another close shave on 54 minutes when Onel Hernandez twisted and turned in the box before getting in a shot that took a deflection and was going in until Tyler Blackett hooked the ball off the line.
Vickers then did well to tip away a curling effort from Marquinhos before Pukki steered the ball agonisingly wide as a Sara corner was allowed to run across the face of goal.
Conor Coventry's deflected shot in the 87th minute, which was comfortably gathered by Angus Gunn, was the best Rotherham could muster in an attacking mode, while Norwich almost snatched all three points in injury time.
When Vickers missed Sara's inswinging corner substitute Christos Tzolis had a clear sight of goal but Wes Harding was on the line to keep his effort out.