Balitsch netted the game's only goal in the 68th minute, lashing home from close range after Per Nilsson's header had hit the bar.
Nuremberg had the first chance of the game in the 12th minute but Hamburg goalkeeper Rene Adler made a fine save from Timothy Chandler's attempt.
Hamburg threatened 12 minutes later but Nuremberg keeper Raphael Schafer was in the right place to keep out Heiko Westermann's header from six yards.
The visitors had two opportunities in first-half stoppage time but Adler fended away Timm Klose's header and then responded in time to stop Alexander Esswein's effort from the rebound.
They nearly took the lead two minutes after the break but Mike Frantz could not beat Adler from seven yards out.
The visitors went close again on the hour mark as Esswein's shot fell to Balitsch, but he headed wide of the empty goal from six yards out.
The breakthrough did arrive midway through the second half, though, as Nilsson's header from a corner landed at the feet of Balitsch, who drilled the ball home.
Hamburg missed a golden chance to equalise four minutes later when Westermann had plenty of space for a header, but Schafer deflected it onto the post and Klose cleared the danger.
HSV almost grabbed a point in stoppage time but Marcell Jansen's header struck the bar.
Robert Mak had the final chance at the other end but his 20-yard shot flew just wide.