The Dons netted three times either side of the interval, with Dave Theobald scoring Cambridge's goal when they were 3-0 down.
In the rearranged first-round game between Braintree and League One leaders Tranmere it was the higher-ranked side who came out on top 3-0.
There was also a penalty shootout at unfancied Slough, who lost out to Mansfield while Lincoln beat Walsall 3-2 after extra time.
The second round takes place on the weekend of December 1 and 2. Click here for the draw in-full.
Results in full: Barrow 1-0 Guiseley, Bradford 3-3 (4-2 pens) Northampton, Braintree 1-3 Tranmere, MK Dons 6-1 Cambridge, Nuneaton 0-2 Luton, Rochdale 0-1 Morecambe, Slough 1-1 (1-4 pens) Mansfield, Walsall 2-3 Lincoln