Huntelaar, who scored eight goals last season, struck in the 13th and 73rd minutes to push his total this season to seven already.
Mladen Petric had equalised the game for Hamburg after 37 minutes.
Schalke's second straight victory comes five days after Stevens returned to the club and moves them into fourth place on 15 points - this win coming on the back of a midweek success in the Europa League.
Hamburg returned to their losing ways after winning their first game of the season last week and remained on four points in last place.
Huntelaar opened the scoring in the 13th minute as Marco Hoger sent a long cross from the right side to the Dutchman, who headed back across the goal from left to right.
Schalke keeper Ralf Fahrmann was forced to make a nice save on a Petric counter attack two minutes later, and Petric's dangerous free kick after 29 minutes was deflected just over the crossbar.
Petric got his goal in the 37th minute for the equaliser after a mistake in the midfield by Benedikt Howedes, leading to Zhi-Gin Lam passing out to Petric, who beat Fahrmann inside the nearly left post.
Raul nearly gave Schalke the lead in the 11 minutes after half-time, but his header went over via the top of the crossbar.
Fahrmann then allowed a Petric shot past him in the 71st minute but was relieved to turn around and find the ball had also skipped past his left-hand post.
At the other end, Hamburg keeper Jaroslav Drobny stopped Raul's header a minute later, but Schalke would grab a lead they would not surrender in the 73rd minute.
Christian Fuchs' cross from the left side went to Huntelaar, who heeled his shot past Drobny, and Schalke held on.