Fourth-placed Schalke increased their gap on fifth side Eintracht Frankfurt to three points, after the latter were held to a 0-0 draw away to Mainz.
But it was the Huntelaar show from 21 minutes onwards, as he fired Schalke ahead with his first goal after Marcell Jansen and Michel Bastos exchanged strikes in the first 10 minutes.
He then completed his treble with goals in the 58th and 66th minutes - increasing his league tally to 10 goals.
Hamburg's defeat was their first in three, leaving them five points behind Schalke and was a dint in their European hopes.
Mainz snapped a three-match losing streak with the draw at home to Frankfurt.