Huntelaar, playing his first game since August after overcoming a knee injury, put Schalke ahead after 34 minutes with his third goal of the season and his 50th in the Bundesliga for Schalke with a well-placed header.
All of the Dutch striker's goals this season have come against Hamburg and his last six have been against the same opponent.
Jefferson Farfan and Max Meyer were also on target to complete the victory and leave Hamburg in the bottom three.
Schalke midfielder Julian Draxler, meanwhile, was not involved, amid speculation linking him with Arsenal.
There was nothing to separate Werder Bremen and rock-bottom Eintracht Braunschweig in Sunday's other game, with both sides wasting chances in snowy conditions in a goalless draw.
Havard Nielsen missed a hat-trick of opportunities on his Braunschweig debut, while Bremen's Philipp Bargfrede missed three chances in the second half and, although Eljero Elia did have the ball in the net late on, his effort was ruled out for offside.
Bizarre Jose Mourinho statement aims to pre-empt punishment after Fenerbahce boss clashes with Galatasaray counterpart
'Andy Robertson has a decision to make as a player, where you either roll your sleeves up and give someone great competition or you accept decisions and say that your time is done.' Alan Shearer on the conundrum facing Arne Slot's Liverpool
