"I'm happy with the hat-trick, but I think the most important thing was the team performance," said the 21-year-old Lasogga after scoring the quickest away hat-trick in 50 years in the Bundesliga.
With the home fans already leaving, Tolgay Arslan rubbed salt in their wounds by returning an attempted clearance from Schaefer for Hamburg's fifth in the 74th.
"We didn't play well at the start, we gave the ball away, but then we got the goal and that's how football is then we started to play," said Hamburg sporting director Oliver Kreuzer.
It was Bert van Marwijk's first victory as Hamburg coach since taking over from the sacked Thorsten Fink.
"I'm only there a week. I've always said I like offensive football, but there are tactics involved too," the Dutchman said.
Hamburg had started the season with four points from six games. Van Marwijk has as many from his two games in charge.
"Five-nil. It doesn't happen every week, but for us it's incredibly important so the confidence comes back. With a victory it happens quicker," Van Marwijk said.
The result piles the pressure on Nuremberg coach Michael Wiesinger, whose side is in the relegation zone without a win this season.
Freiburg is level with Eintracht Braunschweig at the bottom after a 1-1 draw with visiting Eintracht Frankfurt in Sunday's late game.
Nicolas Hoefler scored with five minutes remaining to rescue the draw for the home side, which conceded through Christian Guenter's own goal in the 64th, when an attempted clearance from Oliver Baumann rebounded off the defender.
"If you look at our last games you can see we're always pushing forward, we're playing well. We're just conceding stupid goals," Hoefler said.
Both goalkeepers made crucial saves. Baumann was the busier early on, blocking two shots from Vaclav Kadlec and then thwarting Constant Djakpa.
Kevin Trapp denied Sebastian Freis in the second half but was powerless to stop Hoefler from close range after a corner.
Frankfurt's Johannes Flum was sent off for a second booking in the last minute on his first return since switching between the sides.
"Freiburg did it really well," Flum said of his former side. "They deserved the point. We should have closed it out in the first half."