Germany's Kamke, ranked 98th in the world, shocked Dolgopolov by taking the first set 6-4.
The Ukrainian fought back to take the next two sets 6-1 and 6-1, looking confident going into the fourth.
Kamke broke early in a tense fourth set and, despite a brief fightback from Dolgopolov, took it 6-3.
The German continued his dominance in the final set, again breaking early and looked set to clinch the match until his Ukrainian opponent drew level at 6-6.
Dolgopolov managed to maintain the pressure and clinch the final set 8-6 to reach the third round in Australia.