Kohlschreiber broke Brazilian Thomaz Bellucci's serve five times in a 6-4, 6-2 win; Dolgopolov saved all three break points he faced in a 6-2, 6-4 win against Bernard Tomic and Dimitrov broke Xavier Malisse twice in each set on his way to a 6-3, 6-2 win against the Belgian.
Dolgopolov broke Tomic's serve to improve to 5-1 overall against the Australian. He'll face fifth-seeded Juan Martin del Potro of Argentina in the second round.
Dimitrov plays No. 8 Janko Tipsarevic of Serbia, while Kohlschreiber plays either Frenchman Jeremy Chardy or a qualifier.
Top-ranked Novak Djokovic will decide later whether he will take part in the tournament after twisting his ankle last weekend. He was included in the main draw.
Djokovic injured his ankle while hitting a forehand in his win against Sam Querrey of the United States during a Davis Cup quarterfinal.
He resumed light training on Friday with his coach Marian Vajda and had a short outing against second-ranked Andy Murray in an exhibition match on Saturday.