Darren Purse ended the Bluebirds' goal drought after just three minutes and it was not until early in the second half that Town levelled through Jon Macken.
Purse then grabbed his second from the spot midway through the half only for Ipswich to grab a deserved equaliser in similar fashion when Gary Roberts struck home a penalty five minutes later.
City boss Dave Jones produced a couple of surprises with Kevin Campbell starting in attack in place of Steven Thompson while Kevin McNaughton moved into midfield for the injured Paul Parry.
Former Bluebird Alan Lee was missing from the Ipswich line-up due to a one-match suspension.
Cardiff went ahead two minutes and 20 seconds after the opening whistle when McNaughton took a short corner to Joe Ledley. When the return came in he whipped a cross to the near post where Purse was waiting to flick beyond Lewis Price in the visitors goal.
City's new midfield was working well with McNaughton in particular proving to be a livewire down the left flank, but the visitors were passing the ball around neatly and, on the half-hour, Dan Harding fired a cross-shot that Neil Alexander had to leap high to gather.
It took Ipswich just three minutes of the second half to draw level. City failed to clear a corner and, after Roger Johnson had blocked one effort on the line, Macken was left free to drill in from close range.
The goal lifted Town and they put the hosts under pressure with the result that Thompson was brought into the action along with Kevin Cooper.
The changes had the desired effect and, in the 67th minute when Thompson was elbowed in the area by Jason De Vos, Purse, after a lengthy delay, strode up to rifle the spot-kick into the net.
Within five minutes Ipswich were level, and again it came from the penalty spot, after Roberts was brought down close to the byline. He took the kick himself and sent Alexander the wrong way.
Both sides went looking for the winner but it was the visitors that were the more dangerous on the break and they more than deserved their point.