Hamburg, the only club to have played in the Bundesliga every season since its creation in 1963, secured their first win in four games to move out of the bottom places.
The 21-year-old Lasogga, who joined on loan from Hertha Berlin in the close season, slotted in from the right in the 59th minute and struck twice more including a 67th-minute long-range effort for his first treble at Hamburg.
Captain Rafael van der Vaart, who set up two of Lasogga's goals, had given the visitors a 17th-minute lead with a superb volley and Tolgay Arslan completed the rout in the 74th after a mistake by keeper Raphael Schaefer.
The win lifted Hamburg off the relegation playoff spot and into 14th on eight points. Nuremberg are in 16th on five points.
In Sunday's other match a late Nicolas Hofler strike earned Freiburg a 1-1 home draw with Eintracht Frankfurt.
Treble winners Bayern Munich reclaimed top spot on 20 points on Saturday despite a 1-1 draw at Bayern Leverkusen with Borussia Dortmund suffering their first defeat of the season with a 2-0 loss at Borussia Moenchengladbach to drop to second place on 19.