Under pressure for the most part from a determined Leeds side, Joe Royle's men defended resolutely and made the most of their few chances.
Leeds, meanwhile, wasted their best efforts - including a penalty that was blasted against the bar by Richard Cresswell - and slipped to their first home defeat of the season.
Parkin's first goal came midway through the first half from Ipswich's first meaningful attack. Dean Bowditch gathered a hopeful long ball before delivering a perfectly weighted looping cross across the Leeds box.
Parkin rose the quickest to get to the ball ahead of Paul Butler and headed in from point-blank range to silence Elland Road.
Leeds had been boosted by the return of skipper Butler, Gary Kelly, Eddie Lewis and Shaun Derry before kick-off and started the brighter.
They looked organised going forward and should have taken the lead inside the first ten minutes, only for Rob Hulse to see his close-range header tipped over thanks to superb reactions from Ipswich keeper Lewis Price.
Lewis' shot blasted against the post after 25 minutes following good work from Jonathan Douglas and Hulse to create space for the American.
But instead of kicking on and taking advantage of their dominance, Leeds found themselves chasing the game after Parkin handed Ipswich a shock lead.
Cresswell, starting his first game at Elland Road in the continued absence of suspended hit-man David Healy, wasted his penalty after Jim Magilton tripped Derry inside the box in a moment that typified Leeds' afternoon.
Lewis should have scored after the break but fired straight at Price and Douglas' penalty appeals were turned down by referee Mark Halsey.
Instead, Owen Garvan's delightful touch sent Parkin clear and the under-pressure striker made no mistake with a clinical volley to wrap up a massive win for the Tractor Boys.