Just days after netting a hat trick against Swindon, Jackson and Andy Barcham put the League One side 2-0 up within two minutes before half time
Plymouth pulled one back immediately through Luke Summerfield's freekick but made the 253-mile trip back to Devon empty-handed.
Earlier chances from Curtis Weston and Jackson had given Plymouth a fright and visiting keeper Romain Larrieu had also been forced to race off his line as Barcham got in the clear.
Larrieu also pulled off a great save to keep out a poor clearance from his own defender David McNamee.
But he could do nothing to stop Gillingham scoring twice in the space of two minutes before the break.
Jackson netted the first on 43 minutes as he capitalised on some good build-up play by Barcham and Weston.
Plymouth's hopes of a second round spot in the Carling Cup were dented further still when Barcham headed home Chris Palmer's corner-kick at the far post with 45 minutes gone.
An immediate response was needed and that duly arrived when Plymouth were awarded a dubious free-kick on the edge of the box. Luke Summerfield stepped up and struck low to half the deficit.
Despite the goal it failed to ignite Plymouth. Larrieu kept his side's hopes alive with an 85th minute save from Gills substitute Mark McCammon from point-blank range.
But there was nearly one last twist in the tale as Plymouth hit man Jamie Mackie wasted a golden opportunity to level the scores wide in stoppage time when it seemed easier to score.