Ipswich were further hampered when left-back Ben Thatcher was sent off with a quarter of the game to go for two cautions in a minute, both for fouls on Wayne Routledge.
Cardiff went ahead on nine minutes when Paul Parry's cross found Routledge who returned it back into the centre where Gareth McAuley miscontrolled allowing Jay Bothroyd to pounce with a volley.
Roger Johnson superbly blocked Darren Ambrose's shot and Peter Enckelman saved a Thatcher 30-yarder as Town tried to respond.
Michael Chopra should have doubled the lead when he collected a poor Moritz Volz back-pass and rounded Richard Wright, but McAuley got back to brilliantly clear off the line.
It was 2-0 though on 26 minutes when Parry's free-kick was touched back by Johnson for Gabor Gyepes to fire home.
Ipswich looked stunned for a while, but finally rallied when Jon Walters crossed for Stead to head firmly beyond Enckelman.
Cardiff came close to a third goal on 50 minutes when Bothroyd met a Routledge cross, but Wright pulled off a fine diving save to keep the header out.
Thatcher then saw red for twice bringing down tricky winger Routledge and from then on there was only ever going to be one winner.
Indeed only the woodwork denied Cardiff a third goal when Wright tipped Routledge's cross-shot onto the bar and behind for a corner.