The Bluebirds had new loan signing Eddie Johnson up front as they looked to continue their unbeaten start to the season.
MK Dons won a couple of corners in the opening minutes but the home defence cleared to mount a series of attacks only to fail to trouble former Swansea keeper Willy Gueret.
In the ninth minute, Tony Capaldi went down injured and was replaced by Miguel Comminges.
City were forced to replace the other full-back midway through the half when Darcy Blake left the field and Paul Parry came on.
The first real strike on goal did not come until the 25th minute when Whittingham flashed his shot just wide of the post with Gueret scrambling across his line.
The match came alive in the 41st minute when a cross from Joe Ledley was met by Johnson but Gueret pushed his shot onto the bar.
As the ball came back into play, Riccardo Scimeca was brought down in the box by Drissa Diallo to give the Bluebirds a penalty for the second successive match.
Play was held up as Scimeca received treatment before being stretchered off the field.
Aaron Morris replaced him for his first-team debut and McCormack drilled home the spot-kick to give City a half-time lead.
In the 58th minute, Whittingham doubled City's advantage when he curled a 30-yard free-kick into the net beyond a motionless Gueret.
The Bluebirds now seemed to have the edge, but out of the blue Sean O'Hanlon rose to meet a free-kick and power a header into the net to give his side hope.
The Dons pressed forward in an attempt to force extra time, but the Bluebirds held out and go into the draw for round three.