The Dutchman, who had been out with a knee injury since early March, could not have hoped for a better return with Schalke firmly in control of fourth place which leads to the Champions League qualifying rounds.
Schalke, who have 49 points and are seven behind third-placed Bayer Leverkusen with three games left, terrorised a disoriented Hamburg defence with Huntelaar at the heart of the action from the start.
"Huntelaar had already been working very hard in training," coach Jens Keller said. "We are happy that he is back. It was a well-deserved win even by this score. Now we have taken a small step and given ourselves some breathing space."
Schalke sports director Horst Heldt shrugged off talk of a possible deal with former Bayern Munich player Stefan Effenberg to become their coach from next season, saying no final decision on the future of Keller had been taken yet.
Marcell Jansen's fifth-minute header was quickly cancelled out after the striker, nicknamed 'the Hunter', found Michel Bastos at the edge of the box and the Brazilian wrong-footed keeper Rene Adler with a clever low shot.
Huntelaar then combined with Julian Draxler with a fine overhead kick and completed the swift move, tapping in from close range himself as the Hamburg defence were caught napping yet again.
The forward connected with a perfect Raffael cross with a diving header to give his team a two-goal cushion before heading in his third when Adler palmed a save on to the forward.
Hamburg, who have conceded 16 goals in their last five games, are still in the running for a Europa League spot in eighth place on 44.
The result also leaves Schalke three points ahead of rivals Eintracht Frankfurt, who did themselves no favours with a 0-0 draw at Mainz 05 earlier on Sunday.