Rafael van der Vaart put Hamburg on the way to victory before Lasogga struck three times in seven minutes to put the result beyond any doubt.
With the home fans already leaving the Frankenstadion en masse, Tolgay Arslan added a fifth to complete Hamburg's first away win of the season and only their second overall and heap the pressure on home coach Michael Wiesinger.
Draw specialists Nuremberg - seeking their first win of the season after picking up a point five times - had the first good chance of the game when Tomas Pekhart scrambled the ball wide from close range.
But Hamburg responded and took the lead through Van der Vaart in the 17th minute, the Dutchman volleying in spectacularly from near the penalty spot from Heiko Westermann's cross.
Mike Frantz wasted a good chance to level for Nuremberg early in the second half when he chose to shoot from distance with two players up in support of him.
Nuremberg continued to rally, but a break proved their undoing as Van der Vaart sent Lasogga through and he picked his spot inside the near post to double Hamburg's lead on the hour mark.
The same duo combined three minutes later with Lasogga scoring from close range as he met the Dutchman's corner.
And he completed his seven-minute hat-trick with a shot which struck the right-hand post on its way in, ending any lingering hopes Nuremberg had of recovering.
Four became five when Arslan received the ball from Raphael Schafer's poor clearance and lobbed the ball back over the Nuremberg custodian to make it five in the 74th minute.