BURNLEY have goalkeeper Lee Grant to thank for going into the break goalless.
The 29-year-old reacted quickly to deny DJ Campbell just before the half-hour, shifting his body to get low to his left and tip the striker's volley around the post.
It was the best chance of a half that neither side could stamp their authority on.
Ipswich, smarting from a midweek 5-0 defeat at Crystal Palace, looked tentative at times in Mick McCarthy's first home game in charge.
Burnley were busy around the box, and put plenty of balls into it, but could not make any of their attacking efforts count.
Even Europe's top scorer, Charlie Austin, struggled to make an impact under pressure from central defenders Tommy Smith and Danny Higginbotham.
Chris McCann came close to an early goal after linking with Dean Marney, but dragged a low shot narrowly wide of the near right post.
Martin Paterson later had a close-range shot charged down by goalkeeper Stephen Henderson after a one-two with Marney in the left channel.