The Serbian winger pounced to stab home Paul Connolly's low cross midway through the second half and bring a much needed home win for the Pilgrims, who raised themselves back up to within three points of the play-off zone with a first win in six matches.
The victory was not without cost for Argyle, however, as they finished the game with just ten men after both of their starting full-backs limped out of the action.
On his comeback game at Southend ten days ago, Djordjic scored with a fine early strike in a 1-1 draw and last Saturday he powered home a header in a 2-1 home defeat by Leeds.
The Pilgrims just about shaded a nervy game in which manager Ian Holloway made four changes following the Leeds defeat.
He handed a full debut to young centre-back Gary Sawyer and recalled 18-year-old Luke Summerfield, who turned in a man-of-the-match display.
Argyle midfielder Akos Buzsaky hit the bar with a long-range free-kick in the first half and rattled the same piece of woodwork just before the interval with a header form a Summerfield corner.
Luton's best chances also came in the first half, with strikers Rowan Vine, who returned after suspension, and Warren Feeney each setting the other up in turn for low shots that Argyle goalkeeper Luke McCormick saved well.
The defeat was an eighth successive reversal for Newell's side, a result which equalled a club record that was set in the late 1800s.