The Latvian hit nine aces and broke Dolgopolov's serve twice in each set. He next meets Milos Raonic after the Canadian beat Michael Llodra of France 6-3, 0-6, 6-0.
Gulbis reached the quarterfinals at Doha and the semifinals at Sydney. But the 22-year-old Latvian has won just two matches in the five tournaments since then.
He reached the semifinals on clay at the Rome Masters and the quarterfinals at the Madrid Masters last year.
The 20-year-old Raonic, in his first appearance at Monte Carlo, broke Llodra three times in the deciding set. Raonic had also beaten Llodra at this year's Australian Open, where he came through the qualifiers to reach the fourth round.
"It just sort of took a little bit of figuring out what to do," Raonic said. "I'm still sort of trying to find my game, what the right way to play on clay is for me. I was fortunate enough to get through that one and sort of give myself another chance to pick up more experience in a real match situation."
The big-serving Ljubicic needed little more than an hour to crush Frenchman Jeremy Chardy 6-1, 6-2, and Kohlschreiber rallied past Andrey Golubev of Kazakhstan 5-7, 7-6 (6), 6-4 to set up a match with Roger Federer, seeded second.
Top-ranked Rafael Nadal, who has a bye into the second round, is aiming for his seventh straight Monte Carlo title.