The Spaniard is safely through to the fourth round but he failed to win a game in a stunning first set, before recovering to prevail 0-6 6-2 6-3.
World No 31 Kohlschreiber, 33, was unstoppable in the early stages and romped through the opening set in just 21 minutes.
It was the first time Nadal had failed to win a game in the first set of an ATP Tour encounter since 2008.
But the fifth seed was undaunted and fought back in determined fashion to claim the 822nd win of his career and a last-16 tie against France's Nicolas Mahut, who beat Guido Pella 6-4 6-3.
And he joins an 11-strong group headed by Jimmy Connors (1,535) to have played at least 1,000 matches on tour.
"One thousand matches is a lot of matches," said Nadal afterwards.
"Obviously that's good news, because that says I am having a long career.
"During a lot of years, I heard that I'm going to have a short career, so it's something important for me.
"I remember the first match very well because it was at home in Mallorca. It was my first victory on the ATP and was a great feeling."
Regarding the match itself, Nadal added: "He was doing everything good, so that's sport.
"I lose the set because he was playing too good. That's it.
"But a match is long and the positive thing is I held the pressure well this afternoon, after a very tough first set.
"I resisted well in the first few games of the second set and then I think I played a great second and third set."
