City brought Chris Gunter in at full-back for Kevin McNaughton who was carrying a slight ankle injury, while Glenn Loovens returned in place of Roger Johnson.
Former Bluebirds Neil Alexander and Alan Lee lined up for the Tractor Boys.
A mistake by Darren Purse straight from the kick-off gave Lee a chance on goal, but his lob cleared Kasper Schmeichel and hit the top of the crossbar before being cleared.
City stormed back and from a Parry corner, Loovens appeared to be obstructed in the area but the referee waved play on and then booked the Dutchman for dissent.
Steven Thompson had Alexander stretching to turn an eighth-minute snapshot around the post and then Gunter went close as the Bluebirds continued on the attack.
City were more than matching the visitors with Parry seeing plenty of ball down the right flank, but despite winning a number of corners, they were unable to break down the Ipswich defence.
But they deservedly took the lead in the 33rd minute with a spectacular strike from Parry.
A clever back flick from Thompson sent Gavin Rae into space and he slid a pass out wide to Parry, who was waiting on the wing.
The Wales international cut inside a defender before crashing a shot into the far corner.
Ipswich started the second half by pushing City back into defence, but Purse and Loovens were strong in the centre and restricted the visitors to a couple of corners.
Just after the hour, Joe Ledley was replaced by Peter Whittingham but still the visitors were looking dangerous on the attack.
City's best opportunity came from a Whittingham free-kick in the 78th minute but it shot across goal without anyone getting the final touch.
Then five minutes from time, Parry turned defender when he was on the line to chest away a goal-bound shot from Tommy Miller and the Bluebirds held on for a rare home victory.