Goals from Nick Fenton, Danny Harrison and Drewe Broughton were enough to beat a south coast outfit currently languishing third from bottom.
It leaves Rotherham still unbeaten at their adopted Don Valley home and with only one defeat so far this season.
And the victory marks only the second time in 25 years that Rotherham have made it into the last 16, leaving manager Mark Robins - a League Cup winner with Leicester 11 years ago - with hopes of a money spinning draw.
Defender Fenton and striker Broughton faced an argument over who scored Rotherham's first after 20 minutes until Fenton was handed it after converting an Alex Rhodes corner.
And the home side stretched their lead 11 minutes into the second half when Harrison smashed a spectacular dipping 20-yard effort into the net.
But Saints hit back after 61 minutes when Stern John came off the bench to pull one back with an impressive effort from 25 yards to claim his first of the season.
Rotherham's third goal came after 69 minutes when Broughton got off the mark with his first for the club after drilling in cool shot after good work by Reuben Reid down the right, who laid the ball on a plate for the target man.
Earlier in the piece Saints rarely produced a first-half threat, but Michael Svensson caused a scare for the home side when he headed over.
Rotherham continued to pour forward looking to add to their tally as Saints looked crestfallen at the end, with Rhodes going close to a fourth.