An injury-time penalty from Jordan Hugill – his first goal in Norwich City colours – gave the Canaries all three points at the New York Stadium.
City fell behind to an early goal from Rotherham's Freddie Ladapo and then had to rely on a penalty save from Tim Krul to keep the scoreline at 1-0 going into the break.
However, in the second half a lovely flowing one-touch move got City back on level terms, with an own goal, and then Hugill tucked away a late penalty after the hosts had also been reduced to ten men.