Germany Under-21 striker Pierre-Michel Lasogga needed just eight second half minutes to claim his first Bundesliga hat-trick in a devastating spell as Hamburg scored four goals in just 14 minutes.
"It's great to get the hat-trick, but it's more important that things went so well for the team," said Lasogga, who claimed the fastest away hat-trick in Bundesliga history.
This was only the second game for Van Marwijk, 61, who coached Holland to the 2010 World Cup final.
He replaced Thorsten Fink last month after a disastrous start left Hamburg in the relegation places.
The Dutchman has promised to tighten Hamburg's defence, but it was their attack which ran riot at Nuremberg.
"I like attacking football, although tactical discipline belongs to that and we still lose the ball too often, but it's getting better," said Van Marwijk, whose reign opened with a draw at Frankfurt last week.
"A 5-0 win doesn't happen every week, but it's important to help the self-confidence come back."
Dutch midfielder Rafael van der Vaart opened the scoring with a superb scissor-kick volley on 17 minutes.
The Hamburg captain then provided the final passes for Lasogga to fire home his first two goals while the ex-Hertha Berlin forward completed the hat-trick when he pounced on a loose ball and smashed his shot inside the inside post.
Midfielder Tolgay Arslan bagged the fifth 16 minutes from time to leave Nuremberg reeling.
The rout lifts Hamburg up to 14th, while Nuremberg slip into the bottom three.
On Saturday, European champions Bayern Munich went top for the first time under Pep Guardiola after a 1-1 draw at Bayer Leverkusen.
Bayern extended their unbeaten run to 33 Bundesliga games and are closing in on Hamburg's record of 36, set in January 1983, as the Bavarians returned to the site of their last league defeat in October 2012.
Previous leaders Borussia Dortmund lost top place after suffering a shock 2-0 defeat at Borussia Mönchengladbach earlier in the day.
In a high-tempo clash at Leverkusen's BayArena, Germany midfielder Sidney Sam's 31st-minute equaliser for the hosts cancelled out Toni Kroos' opening goal for Bayern.
Leverkusen goalkeeper Bernd Leno guaranteed a point for his side by denying Franck Ribery twice in as many second-half minutes, then Mario Götze, while Thomas Mueller had a penalty appeal turned down.
But Guardiola was a picture of frustration, brooding on the Bayern bench and drumming his fingers as Bayern enjoyed 27 shots on goal and 78 percent possession, but managed just a single goal.
The point was enough to send Bayern top, with Leverkusen third, behind Borussia Dortmund.
Fresh from their impressive 3-0 Champions League win over Marseille, Dortmund were set to claim an away point until a disastrous final 10-minute spell, triggered by Mats Hummels' red card.
The Germany defender was sent off on 81 minutes after a reckless challenge on 'Gladbach's Norway midfielder Havard Nordtveit in the area.
Germany striker Max Kruse netted the resulting penalty, then Brazilian forward Raffael hit their second four minutes from time to see 'Gladbach move up to fourth.
Schalke 04 came from behind to claim a 4-1 win over 10-man Augsburg in Gelsenkirchen to move up to eighth.
VfB Stuttgart dropped to seventh after their 1-1 draw at home to Werder Bremen while Hoffenheim stayed 10th with a 2-2 draw at Mainz.
Eintracht Braunschweig, who have been bottom of the table since last season's promotion, picked up their first win of the season with a shock 2-0 victory at VfL Wolfsburg – their first Bundesliga victory since 1985.
Despite the win, Braunschweig stay bottom of the table on goal difference but level on points with 17th-placed Freiburg who drew 1-1 at home to ten-man Eintracht Frankfurt on Sunday.
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