Paraguay international Lucas Barrios scored twice and Kevin Grosskreutz, Mats Hummels and Robert Lewandowski added one apiece to lift Dortmund to 12 points with their fourth straight win, three behind Mainz who beat Cologne 2-0 on Tuesday.
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"If we said before the season that at this stage we would have 12 points we would have said: yeah right," said Dortmund coach Jurgen Klopp.
"Twelve points are a dream that the team deserves but worked hard to get."
Last season's runners-up Schalke 04 notched their first three points thanks to Dutchman Huntelaar's 86th-minute winner but having lost their first four games they remained bottom of the table.
Barrios opened their account with a well-placed shot before Grosskreutz took the wind out of the visitors' sails with a curled strike from the edge of the area seven minutes before the break.
Klopp's team could have added a handful of goals before Hummels made it 3-0 with a header just past the hour as the visitors collapsed under their rivals' continuous pressure.
"This win is a relief," said Schalke coach Felix Magath, who had been under mounting pressure after spending big during the transfer period.
"We were under pressure. I am satisfied with my team though you could still sense their insecurity."
