The visitors made a bright start with Paul Parry firing across goal seconds into the game, before Jeff Whitley's angled shot was held by Price.
Ipswich's first chance came on six minutes when debutant Darren Purse, the Cardiff skipper, felled Ian Westlake on the edge of the box and Town captain Jim Magilton floated a curling effort narrowly wide.
Cameron Jerome was a danger for Cardiff throughout and he rose above Matt Richards to glance a header just wide from a Neal Ardley cross before Jason De Vos had to time his challenge well to stop Jerome breaking through.
Owen Garvan shot over for Town before another new arrival Sam Parkin chested a long ball beyond Cardiff goalkeeper Neil Alexander, but he went too wide and could only shoot into the side-netting.
Forster had a shot easily gathered by Alexander before Town should have gone ahead just before the break, Forster's pull-back being deflected perfectly for Parkin, but his weakly hit shot was easy for the keeper.
Jerome looped a header narrowly over just before the break, and straight after it he latched onto a loose Ian Westlake pass before having his shot charged down by De Vos.
Kevin Cooper saw a 30-yard free-kick deflected onto the roof of the net before Town went ahead after 64 minutes when Forster ran in unmarked to volley home an inswinging Darren Currie free-kick.
A minute later Forster burst down the left onto a long Magilton pass and found Parkin with his pull-back, but after flicking the ball up with his first touch, he dragged the shot wide with his next.
Cooper fired a firm drive not far over for Cardiff before play switched to the other end and Richards crossed for Parkin to send in a firm header, which was too easy for Alexander.
Town had two chances to seal the points inside the last ten minutes from Currie corners as first Parkin headed against the outside of the post from six yards, then from even closer Richard Naylor dived in to guide an unchallenged header wide.
Whitley fired over from a pass from substitute Alan Lee as Cardiff tried to punish Town's wastefulness before Currie curled a free-kick off target for Ipswich.
Parkin shot over after racing forward and cutting inside the last defender before Cardiff had the chance to steal a point in the dying moments of the game.
Neal Ardley pumped a free-kick into a crowded box which Lee controlled and turned to fire in a firm shot from around six yards, but Wales Under-21 goalkeeper Price made a magnificent reaction save and Naylor booted the loose ball clear,
There was a concern for Ipswich as the game went into the final minute with De Vos down and looking in pain after falling awkwardly, but he was able to complete the game and help earn his side a welcome opening day win.
The visitors will feel a little hard done by, having defended well for long periods, but no doubt they will improve once new boss Dave Jones has got his multitude of new signings gelled together.