Lasogga opened his account for the season with the only goal of the game 10 minutes before half-time on Saturday to send Dortmund crashing to a third defeat in a four-game winless league streak.
The 22-year-old was instrumental in keeping Hamburg in the Bundesliga last term and was also on target in a 3-0 home success over Dortmund when the sides last met in February.
Dortmund heaped on the pressure late on with both Adrian Ramos and the in-form Pierre-Emerick Aubameyang going close, but the Hamburg defence held firm to grind out a priceless first league win of the season.
Much has been made of Dortmund's poor start to the Bundesliga and Jurgen Klopp's men were sluggish in the early stages against struggling Hamburg.
World Cup winner Mats Hummels made his first home start of the season in front of a typically vibrant Signal Iduna Park crowd, but it was the visitors who imposed themselves during a scrappy opening period.
Josef Zinnbauer's start to life at the Imtech Arena has been a difficult one, but Nicolai Muller, Hamburg's only scorer this season prior to kick-off, almost put the away side ahead after 11 minutes.
The 27-year-old broke through the Dortmund defence only to skew his effort wide from a tight angle under pressure from goalkeeper Roman Weidenfeller.
But Muller atoned for that miss after 35 minutes when more lacklustre defending from Klopp's side gifted Hamburg the opener.
Muller latched onto Ramos' loose pass in midfield before gliding through Dortmund's gaping defence and allowing Lasogga to slot into an empty net.
Lasogga's goal was no less than Hamburg deserved and Lewis Holtby nearly extended their lead on the stroke of half-time, but his close-range header was just wide.
Just as in the first half, the second period got off to a low-key start.
Despite Dortmund enjoying plenty of possession, Hamburg countered well to keep Weidenfeller busy.
Weidenfeller had conceded six times in his previous three Bundesliga outings heading into Saturday's clash, but was in top form to parry away a powerful header from Heiko Westermann.
At the other end, Hamburg counterpart Jaroslav Drobny was not to be outdone, with the Czech Republic international producing a first-class save to prevent Ramos' diving header from finding the bottom corner in the 71st minute.
That chance rallied Dortmund and they went close again moments later as Sebastian Kehl fired his effort just wide as the game approached a frantic climax.
Ramos saw his rasping long-range strike held by Drobny as the late Dortmund onslaught proved frivolous.
