Rockbottom Ipswich went behind inside the opening minute when loanee Ross Barkley tucked home a loose ball.
Michail Antonio twice came close to doubling the lead in the opening quarter of an hour. The winger first saw a shot fizz just wide before his looping header was cleared off the line by Danny Higginbotham.
Ipswich's best opportunities in the opening half came from free kicks but Higginbotham and Aaron Cresswell both squandered the set pieces.
The visitors had another clear-cut chance when Chris O'Grady was left unmarked in the area but he headed wide of the goal.
The Blues were soon two behind though, when Everton youngster Barkley found the bottom corner with a vicious strike.
Ipswich did little to get back into the match and they went three down nine minutes from time when Antonio rounded Stephen Henderson and rolled home.
The Tractor Boys, who are searching for a new manager, are now five points from safety as Wednesday climb out of the drop zone.