City were 2-0 ahead at the half-time break but Ipswich substitute Jason Scotland has pulled a goal back in the 57th minute as the visitors improved after the break.
It took an injury-time goal from Stewart to finish off the job.
Nick Barmby rotates his squad with Robbie Brady, Joe Dudgeon and Richard Garcia earning rare starts and Seyi Olofinjana and Jay Simpson on the bench,
Vito Mannone starts in goal after joining on loan from Arsenal in midweek as Peter Gulacsi is out for eight weeks with a knee injury. Martin Pusic is also out.
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