Heading into the game, the Bookmakers had the League 1 hosts as favorites for the game, and that proved to be the correct decision.
Goals from Cameron Humphreys, Conor Chaplin from the spot, Freddie Ladapo and a late Wes Burns penalty were enough to see the Tractor Boys through.
Conor Washington had briefly drawn the Millers level from the penalty spot two minutes into the second half.
Despite dominating the first half, it took until the 43rd minute for Ipswich to take the lead when Humphreys stroked home after good work from Kayden Jackson and Ladapo.
The Millers drew level straight after half-time when Washington was brought down in the box by Richard Keogh and stepped up to send Vaclav Hladky the wrong way from the spot.
The Tractor Boys had a penalty of their own when Ladapo was dragged down by Wes Harding and Chaplin stepped up to put the home side in front.
Ladapo had a goal of his own minutes later, rounding Rotherham goalkeeper Viktor Johansson before slotting in against his former club.
There was still time for Ipswich to add a fourth, with Burns smashing his spot-kick straight down the middle after Marcus Harness had been felled.