The visitors looked set for three points thanks to Paul Huntington's first-half opener.
But substitute Parkin earned the Hatters a vital point by touching home Dean Morgan's cross with just seconds remaining.
The clash marked Mick Harford's first home game in charge of Luton and the hosts started brightly with ex-Leeds man Matthew Spring hitting a deflected 20-yard shot just past the post early on.
Leeds soon settled though and should have gone ahead in the 13th minute when Tresor Kandol almost netted against his former employers.
The striker got away from Keith Keane to run on to Peter Sweeney's pass and sent in a lob from the edge of the area which sailed over goalkeeper Dean Brill, but also the bar.
Luton responded with a sustained period of pressure on the visiting rearguard with their best moment coming in the 25th minute as Steve Robinson set up Paul Furlong to have two shots blocked before Alan Goodall smashed the rebound off target from 20 yards.
Leeds rode the storm though and took the lead themselves from a well-executed set-play two minutes later.
Chris Perry fouled Jermaine Beckford on the edge of the area and, from Sweeney's resulting free-kick, Huntington got free of his marker to nod home from 12 yards.
That was about all the action the first half had to offer as Leeds defended deeply.
The visitors were happy to soak up more home possession after the interval and the tactic worked perfectly as Luton huffed and puffed without ever really threatening while the visitors twice should have scored on the break.
Beckford raced clear and rounded Brill in the 63rd minute only to fire wide from a tight angle and Kandol ran through from Andy Hughes' pass in the 78th minute only to blaze over with just Brill to beat.
Leeds were made to pay for their misses as Parkin stepped off the bench to convert fellow substitute Morgan's cross in stoppage time to send the home fans delirious.