The win lifted Hamburg, who needed a relegation playoff to stay up last season, to seventh on six points.
Gladbach, third in the Bundesliga last season, will go into their maiden Champions League group stage match at Sevilla on Tuesday in abysmal form and with the pressure piling on coach Lucien Favre.
The visitors took the lead when Lasogga, who struggled with injuries and form last season and has been relegated to second choice this term, pounced on Tony Jantschke's miscued pass before rounding keeper Yann Sommer after 11 minutes.
The 23-year-old striker, who is battling against Ivica Olic and Sven Schipplock for a place and was making his first start of the season, doubled the lead just before the break when he headed in a corner.
Nicolai Mueller chipped Sommer with a delicate first touch from Hamburg keeper Jaroslav Drobny's 60-metre kick to grab a spectacular third goal early in the second half.
On Saturday, Bayern Munich take on Augsburg while fellow co-leaders Borussia Dortmund meet Hanover 96 as both teams look to maintain their 100 percent starts.
(Reporting by Karolos Grohmann,; Editing by Tony Jimenez)
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