The frontman, who is on loan from Premier League Blackburn, hit two superb strikes either side of the break to earn the Pilgrims' second victory in four days, though Paul Sturrock's side were forced to endure a late scare when Paddy McCarthy grabbed a late consolation for Neil Warnock's men.
After a tepid opening, the game burst into life in the 24th minute after Ben Watson's corner was headed goalwards by Clint Hill, only for Luke Summerfield to clear off the line.
Two minutes later Palace forward Alan Lee was forced to head over from under his own bar after Summerfield's dangerous inswinging corner.
But just seconds later, Gallagher notched his first of the afternoon after sweetly slotting home Summerfield's clever corner from the edge of the box to give Argyle the lead.
Palace twice came very close to snatching an equaliser on the stroke of half-time, first with Paul Ifill's spectacular first-time volley which was tipped over by Romain Larrieu and moments later from Lee whose instinctive shot from ten yards was well held by the Argyle keeper.
The home side came flying out of the blocks after the break and three minutes in half-time substitute Victor Moses hit a superb 25-yard volley that Larrieu tipped over and seconds later Shaun Derry grazed Argyle's right-hand post with a low drive.
However, dangerman Gallagher soon dashed any hopes Palace had of getting back into the game after he was allowed too much room on the edge of the box before smashing a low 20 yard drive past Speroni in the 56th minute to double Plymouth's lead.
Summerfield came close to adding a third after his drive from the edge of the box flashed just wide in the 66th minute, before Ifill's goalbound shot from 12 yards hit Mathias Doumbe square on the chest.
McCarthy dragged Palace back into the game in the 85th minute after heading home Watson's corner, but it was too little to late for the home side who have recorded just one Championship victory this season.