A first-half strike by Alan Mahon was enough to clinch all the points, but they should have won by a bigger margin after Shefki Kuqi tossed away two great chances to score and Pablo Counago missed a penalty.
City started brightly, testing the visitors after only five minutes when Andy Gray ran on to Tom Kearney's pass and struck an angled shot inside the box, but keeper Kelvin Davis managed to get is body behind it.
Moments later, Mahon could have opened the scoring for Ipswich with a well-struck shot from close range, but City keeper Marlon Beresford was more than equal to it, pulling off a fine save to deny him.
City boss Nicky Law was forced to re-jig his defence after only seven minutes, with Wayne Jacobs replacing Paul Heckingbottom, who injured himself after a firm challenge on Counago.
Kuqi squandered a golden chance to put Ipswich ahead after 17 minutes. The Finnish international picked up a harmless throughball, shrugged off Wayne Jacobs and raced into the box.
But with only the keeper to beat, he rifled his shot over the bar.
City almost made him pay for that after Gray whipped over a dangerous cross from the right. Richard Naylor managed to flick to ball out of the box.
Ben Muirhead latched on to it but his shot drifted wide off the target.
Ipswich always showed more composure of the ball and they should have taken the lead after Mahon drilled a free-kick into the area, finding Georges Santos only six yards out, but the big defender somehow put his header wide.
Kuqi then saw his stinging shot beaten away by Beresford before Bradford hit back with their best move of the half. Nicky Summerbee was freed down the right and picked out Luke Cornwall with a pinpoint cross, but the young striker could not get enough power on his shot to trouble Davis.
Town finally broke the deadlock three minutes before the break.
Counago cushioned the ball with his head following a long ball into the box and planted it into the path of Mahon, who drove a left-foot shot past Beresford's near post.
After the break, Ipswich continued to play the better football. Kuqi once again let himself down with an awful finish after he amazingly screwed a six-yard shot wide.
Mahon was then unlucky not the score his second goal when Beresford tipped away his well-taken free-kick.
City were then hit with another injury blow. This time Jason Gavin went off clutching his shoulder after 63 minutes.
Jim Magilton and Counago both had chances to wrap up the points with close-range headers, but on each occasion, Beresford kept them out with instinctive saves.
The visitors refused to let up, and they were rewarded with a penalty after 74 minutes when David Wetherall pulled down Kuqi. But Counago's spot-kick was brilliantly saved by Beresford.
City, given a new lease of life after being let off the hook, put Ipswich under pressure.
Muirhead first unleashed a powerful drive that whistled past Davis' left-hand post, then sub Danny Forest broke into the box, but just as he was about the shoot, Fabian Wilnis made a stunning tackle to win the ball and put it out for a corner.
City pressed for an equaliser during six minutes of stoppage time, but Ipswich clung on to win.