Parkin was on target after just three minutes to net his second of the season as Luton made the first step to reduce their 30 point deduction.
With a starting line-up featuring seven summer signings, Mick Harford's men surprisingly struck up an immediate understanding which led to Parkin's opener.
Rossi Jarvis' deflected pass released Chris Martin down the left flank and the striker's clipped cross was met by the unmarked Parkin at the far post, who guided his header passed Alan Julian.
Luton proceeded to pepper the Gillingham defence with several waves of attack as the home side struggled to come to terms with their slick passing moves.
Mark McCammon had a chance to level for the Gills but completely misjudged his header from John Nutter's free-kick.
Five minutes before the interval, McCammon narrowly failed to squeeze home Tyrone Berry's cross from three yards out, before his looping header from Barry Fuller's delivery crept just wide of Dean Brill's post.
Chances continued to fall to the tall Barbadian and on 54 minutes he combined again with Nutter only to see another header hacked off the line by Sol Davis.
Luton continued to soak up the home side's pressure but were lucky to escape in the 74th minute when both Andrew Crofts and Simeon Jackson failed to convert a mammoth goal-mouth scramble with Jarvis and Brill producing brilliant blocks to deny them.
Martin came close to punishing Gillingham's woeful finishing a minute later, but his speculative drive flashed just wide of Julian's far post.
The goalkeeper threw himself forward as his side launched a final attack but his efforts were in vain as the final whistle signalled the start of Luton's plans for a great escape.