Goals from Phil Foden, Jadon Sancho, Lukas Nmecha and Demeaco Duhaney saw Lee Carsley’s side safely into the last eight of the traditional competition.
Southampton started the brighter of the two sides with Aro Muric forced into an excellent low save from Jonathan Afolabi’s strike inside the first five minutes.
However, City soon returned to their comfort zone in control of the possession with Nmecha and Sancho testing Adam Parkes in the Southampton goal.
That pressure soon told as Phil Foden collected the ball in the inside left channel and fired across the goal to put City in the lead.
One became two shortly before half-time as Brahim Diaz drilled a cross along the floor for Sancho, who made no mistake this time from around 10 yards out.
There was still time for a third before the break with Lukas Nmecha on hand to tap home Demeaco Duhaney’s inviting ball across the face of goal.
The one-way traffic continued in the second period with a number of near misses for Sancho and Nmecha, who had the visitors on the edge throughout the night.
The fourth did inevitably come, although the scorer was perhaps a surprise. After Tom Dele-Bashiru's drilled effort hit the post, Demeaco Duhaney was presented with the opportunity to tap home and seal City's passage.