There was a let-off for the visitors in the fifth minute when Konstantin Rausch hit the crossbar with a free kick from outside the area, and the hosts kept the early pressure up.
Hamburg soon found their rhythm and started bombarding the visitors goal, but they needed a penalty to break the deadlock.
Niemeyer was penalised for a foul in the box just before the half-hour mark, allowing Lasogga to step up and fire into the bottom corner.
Darmstadt were level two minutes into the second half, Heller popping up in the six-yard box to head Jerome Gondorf's cross into the bottom corner.
Rausch had another attempt from a free kick two minutes later but Rene Adler made the diving save.
Shots from Lasogga and Lewis Holtby missed the target as both teams struggled to test the opposition goalkeeper.
Heller had a golden opportunity to win the match in stoppage time but Adler stopped his shot from point-blank range.