Aro Muric was the penalty shoot-out hero as City gained two points in their group stage opener at the New York Stadium.
The keeper – who was outstanding throughout – twice denied Rotherham from 12 yards as Lukas Nmecha, Matt Smith, Taylor Richards and Charlie Oliver converted to give the Blues a bonus point win.
City had fought back to take the game to penalties – after 90 minutes under competition rules – as substitute Benjamin Garre equalised in the final minute of stoppage time to cancel out David Ball’s 64th minute strike.
In an evenly contested first half City went close twice through Nmecha.
The captain had the first real chance as he turned sharply and pulled the trigger in the six yard box only to see his shot blocked.
Muric was called into action soon after, denying Ball from point blank range with his legs, as Rotherham looked to make their possession count.
City were threatening on the break – with Smith and Jacob Davenport doing their best to unlock the opposition’s defence and the former did for the best chance of the half, when Nmecha raced clear but fired the resulting shot into the side netting.
After the break Paul Warne’s side came into the ascendancy, with Muric and his defence required to be at their best.
The keeper was at full stretch to deny Jonson Clarke-Harris and Jon Taylor, but ex-City youngster, Ball, found a way through.
Alex Bray won possession deep in the Blues’ half and played a precise through ball, which the forward duly gathered before calmly converting.
The Yorkshire outfit continued to press and might have extended their lead if not for a last ditch block by Smith, but City rallied late on.
Substitute Rabbi Matondo flashed a shot across goal before Garre – deep into added time – found a yard of space in the box and fired home into the bottom corner to level and send the tie to penalties.