Dortmund came into the game at Signal Iduna Park sitting at the foot of the table, following a run of just one win in their past 10 league outings.
But last season's runners-up secured a much-needed victory, Ilkay Gundogan's first goal for the club since July 2013 lifting Dortmund out of the relegation zone and up to 14th place.
Pierre Emerick-Aubameyang was unfortunate to see two goals ruled out for offside in the second half - one a clear mistake from the officials and the other a very tight call.
There was one late scare when Dortmund survived vociferous appeals for a penalty after Neven Subotic tangled with Tarik Elyounoussi in the area, but Hoffenheim's protests were waved away and Klopp's men managed to hold on.
"I feel relief!" Klopp told reporters afterwards. "The happiness will come later.
"It was a really intense game. We must continue to work. We had an enormous amount of luck in the penalty situation. And insane bad luck too with the offside situation.
"In terms of points, we still do not have a fantastic yield, but the three were the maximum.
"It was a good game and a deserved victory. But it is only one.
"The atmosphere was unique. Thank you for this. Let's keep going!"
