Lasogga's 35th-minute strike was all that separated the two teams at Signal Iduna Park as Hamburg upstaged a lacklustre Dortmund 1-0.
The result helped Hamburg off the foot of the table, while it ended the club's dismal winless streak, having not tasted victory since April - a run of 11 matches spanning back to last season.
Lasogga felt Hamburg were the better team despite weathering a Dortmund onslaught during the closing stages.
"We put in a fantastic team performance today, and even though it was a bit hairy at the end, in my opinion, we were deserved winners," the 22-year-old said.
"I'm obviously delighted to have scored, but the most important thing to come out of today was that we got the reward our effort deserved.
"It's been clear over the last three games that we're heading in the right direction and today we got the three points to prove it."
Hamburg winger Nicolai Muller and right-back Dennis Diekmeier were both relieved to collect maximum points heading into the international break.
"We stayed calm and had a plan which we tried to implement," said Muller.
"Games like today's, ones which are on a knife-edge throughout, can sometimes fall in the other direction. We worked to make sure that didn't happen.
"If we keep playing like that, then we'll keep picking up points. Above all, we've got to stay focused and keep working hard."
Diekmeier added: "I thought to myself: Please, please let us win this one. We put so much effort in that it had to be rewarded.
"Now we've got two weeks to work hard, with the confidence of a positive result behind us. That always makes things easier."
