The Hatters looked to be on their way to a hard-fought win thanks to Warren Feeney's 63rd minute header.
But Argyle earned a draw when Djordjic headed home fellow substitute Matt Derbyshire's deep cross at the death to create a virtual carbon copy of the game fought out when the sides last met two seasons ago.
Town welcomed back skipper Kevin Nicholls as he returned in midfield for Steve Robinson after missing Tuesday's thrilling 4-2 win over Norwich.
Sol Davis made the starting 11 despite picking up hamstring and ankle knocks against the Canaries.
Boosted by their midweek victory, Luton started swiftly and registered the first attempt on goal after just two minutes when Steve Howard flicked on Carlos Edwards' throw and Feeney hit a snapshot at Romain Larrieu.
That might have been little more than a warning shot across the Argyle bows, but four minutes later Town should have taken an early lead.
Ahmet Brkovic collected a half-cleared corner and squared to Davis to chip into the path of Chris Coyne running clear into the penalty area and the defender took a touch before poking a shot straight at Larrieu from ten yards.
The Hatters continued to press and Feeney had three efforts all fly off target in the space of eight minutes before he really should have found the net in the 19th minute.
Hasney Aljofree stumbled when trying to control a long Davis pass and Feeney nipped in to sprint clean through on goal, but after rounding Larrieu the Northern Ireland international pulled his left-foot shoot wide from an angle.
Luton almost paid the price for the miss immediately as visiting skipper Paul Wotton played in Scott Taylor and Marlon Beresford had to be quick of his line to block at the striker's feet.
Plymouth finally tightened up until a slick Hatters move down the left in the 29th minute.
Feeney, Davis, Holmes and Howard were all involved before Holmes swivelled to cross for Feeney, who could only direct his header straight at Larrieu.
Despite Luton's dominance it was Plymouth who ended the half on the offensive when Akos Buzsaky played a one-two with Taylor before driving just over the bar from 15 yards in stoppage time.
After a scrappy opening to the second period, Luton introduced Kevin Foley for Dean Morgan in the 55th minute in attempt to freshen things up.
And it almost prompted an immediate Town goal as Nicholls' inswinging free-kick from the left was nodded just wide by Markus Heikkinen.
Heikkinen then repeated the trick two minutes later as he headed another Nicholls place kick over the bar.
Enoch Showunmi was next to enter the fray for Brkovic, but it was Feeney who broke the deadlock in fine style in the 63rd minute.
Howard combined well with Edwards down the right and from the Trinidad & Tobago international's deep cross Feeney rose to head powerfully into the far corner from 12 yards for his fifth of the season.