The 21-year-old struck either side of half time to seal the points for the Eagles in a match where he once again proved he has a strong case to play a big role in Chelsea's first team next season.
Salomon Rondon thought he had given the visitors a lifeline after James Tomkins netted Palace's second, but Gallagher sealed the points late on with a superb curling effort late on to end Palace's three-match losing streak.
The result means Everton have now won just one match in ten outings - their victory over Arsenal last time out - and Benitez will once again come under fire for his side's lacklustre showing.
Gallagher, though, was once again superb throughout and it was the Chelsea loanee who gave the hosts a deserved lead shortly before half-time.
The 21-year-old capitalised after a sloppy pass from Demarai Gray gifted Palace the ball and he arrived in the perfect position to fire home in the middle of the box.
It was his fifth goal of the campaign and one that once again demonstrated reinforced his chances of getting a run in Thomas Tuchel's first team next term.
Palace doubled their tally shortly after the hour mark when James Tomkins nodded home from an inch-perfect delivery from Will Hughes.
But the Toffees gave themselves a lifeline ten minutes later when Salomon Rondon made an immediate impact off the bench to tap home from close range and give the visitors hope of another comeback.
Unfortunately, it was too little, too late for the Merseyside outfit, who did nowhere near enough to test Palace's resolve throughout the clash.
And Gallagher topped off another fine performance with a superb strike late on to seal the points for his side.
The result means Everton remain in 14th in the top-flight after suffering their eighth defeat of the campaign.
Palace, meanwhile, have moved up to 12th with the victory to continue what has been an impressive start to the season from Patrick Vieira's side.