The Dutchman, who last played on August 17 against VfL Wolfsburg when he suffered torn knee ligaments, continued his prolific scoring run against Hamburg with his 10th goal in seven games against the northern club.
"We were very aggressive and were dominant throughout," Huntelaar told reporters. "We have a good team and we want to clinch a spot in next season's Champions League."
Schalke, who moved up to fifth place on 31 points as the league resumed after the winter break, looked hungrier at the start and Huntelaar could have put them ahead after 23 minutes but for a last-gasp challenge by defender Heiko Westermann.
The 30-year-old did better in the 34th, connecting with a fine Jefferson Farfan cross to nod past keeper Jaroslav Drobny.
Hamburg, whose striker Pierre-Michel Lasogga and full back Zhin Gi Lam limped off injured, were livelier after the break but a defensive blunder between Marcell Jansen and Drobny allowed Farfan, who was involved in every Schalke goal, to sprint through and slot into an empty goal in the 53rd minute.
Max Meyer knocked the hosts out with a quickfire third goal three minutes later after yet another fine run down the wing by Farfan, triggering a mass exodus by the home fans amid freezing temperatures.
Hamburg, the only club to have played every season in the top division since the Bundesliga's creation in 1963, are in the relegation playoff spot on 16 points following their fourth straight defeat.
Werder Bremen and bottom-of-the-table Eintracht Braunschweig shared the points in a goalless draw.
Bayern Munich extended their lead at the top of the table to 10 points with a 2-0 victory over Borussia Moenchengladbach on Friday and second-placed Bayer Leverkusen suffered a last-gasp 3-2 defeat by Freiburg.
Borussia Dortmund climbed up to third place on 33 points, four behind Leverkusen, despite a 2-2 draw against visiting Augsburg on Saturday.