Latvian Artjoms Rudnevs snatched a 70th minute lead scoring at the far post after a lacklustre first half by the visitors.
Their joy was short-lived, however, with Tomas Pekhart slotting in the equaliser following a well-timed cutback in the box by Timo Gebhart five minutes later, with Nuremberg coach Michael Wiesinger making a successful debut.
Despite the return of playmaker Rafael van der Vaart, Hamburg were toothless in the first half with the Dutch midfielder, back from a muscle injury, looking far from top form.
They dominated throughout after the interval and poured forward in the last 20 minutes but keeper Raphael Schaefer made several superb saves and Son Heung-Min headed on to the woodwork in the last minute as Nuremberg, who are in 15th place, earned a point.
In the day's other game FC Augsburg boosted their hope of survival with a 3-2 win at fellow struggles Fortuna Dusseldorf.
It was Markus Weinzierl's side first away win of the season.
Bayern Munich are nine points clear at the top after their 2-0 win over Greuther Fuerth on Saturday with Bayer Leverkusen, on 36 points, beating Eintracht Frankfurt 3-1 to remain second.
Champions Borussia Dortmund crushed Werder Bremen 5-0 to move up to 33 points in third place.