However, the 30-year-old Nadal won the opening game of the second set, sending him on his way to an 0-6, 6-2, 6-3 victory on Sunday.
It was Nadal's 1,000th career match. Nadal is now 14-1 in matches against Kohlschreiber, but he struggled to win this one.
Nadal left the court after the first set and returned a different player. The Spaniard hit a forehand down the line for a hold in the opening game of the second set, then broke serve for the first time in the sixth game to take control of the match.
Nadal's next opponent will be Frenchman Nicolas Mahut, who beat Argentine Guido Pella 6-4, 6-3.
Second-seed Kei Nishikori of Japan had to get through a three-setter to advance as well. He edged Fernando Verdasco of Spain 7-6 (2), 6-7 (5), 6-1 in two hours and 44 minutes.
"It was definitely a long match," Nishikori said. "It wasn't easy in the third set, but I have a day off tomorrow, so I should be OK."
The 27-year-old Nishikori fired 37 winners, but Verdasco induced him into 48 unforced errors.
Nishikori took a quick 3-0 lead to open the match but ultimately had to go to a tiebreaker to win the opening set.
The Japanese player served for the match at 5-4 in the second set, but Verdasco would save a match point before breaking serve and eventually winning that set in a tiebreaker.
Nishikori dominated the third set.
"I knew it's going to be a tough one," Nishikori said. "Fernando is a very solid player. He has a great serve and great groundstrokes. I knew it was going to be long rallies.
"But it was a shame when I was up a break in both first and second sets and both went to 7-6. That was something I made some mistakes when I was up a break. But in the third set, I was very focused."
Nishikori next faces Federico Delbonis of Argentina, who eliminated Jan-Lennard Struff of Germany 7-6 (5), 6-1.
Third-seeded Milos Raonic of Canada was forced to withdraw before beginning his third-round match against American Jared Donaldson because of a hamstring injury.
"It's related to the previous injury I sustained almost four weeks ago, if not a little bit more than four weeks ago, in Delray Beach," Raonic said. "It's the same muscle in the hamstring up high. It got progressively worse after my first round, after practicing yesterday, and it seemed like it was not possible for me to compete today without putting myself at significant risk.
"Right now the perspective is going to change a little bit. Obviously, the goal through these tournaments being on hard courts was that I can come back as soon as I feel ready. I think that that perspective is going to change to come back when I feel like I'm 100 percent. That could be in two weeks; that could be a little bit longer. I think the ideology behind when I'm back playing matches and competing, it will be in the sense that that's the best shape my body could be in."
Raonic was forced to pull out of the BNP Paribas Open earlier this month due to the same injury.
In other matches, Donald Young of the United States recorded a 7-6 (2), 6-4 victory over Benoit Paire of France, and he will now play Italian Fabio Fognini, who outlasted Frenchman Jeremy Chardy 3-6, 6-4, 6-4.
Jack Sock, an American seeded 13th, brushed aside Jiri Vesely of the Czech Republic 6-3, 7-6 (0).