World number 31 Kohlschreiber was on fire early, ripping through the first set in only 21 minutes but fifth seed Nadal flipped the switch and turned the match on its head to prevail 0-6 6-2 6-3 on the main stadium hard court at Crandon Park.
It was the first time Nadal had failed to win a game in the first set of an ATP tour match since 2008, the ATP said.
The 30-year-old Spaniard ignited the near-capacity crowd with a typically determined comeback to clinch his 822nd career victory.
Nadal joins a small group of 11 players headed by Jimmy Connors (1,535) to have played at least 1,000 matches. He told reporters:
One thousand matches is a lot of matches. 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.
Nadal said he had not done much wrong in the first set against an opponent who was in the zone.
"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."
While Nadal played in the relative comfort of the late afternoon, Kei Nishikori also took three sets and nearly three hours to advance under a high noon sun, outlasting Spain's Fernando Verdasco 7-6(2) 6-7(5) 6-1.
Nishikori, the runner-up to Novak Djokovic last year, fired 37 winners but Verdasco, aided by persistent swirling winds, used his varying pace and depth to rattle Japan's number one, inducing 48 unforced errors.
Milos Raonic withdrew before his match against American qualifier Jared Donaldson, blaming a persistent hamstring injury.
"It's related to the previous injury I sustained almost four weeks ago... in Delray Beach," the Canadian told reporters.
Raonic said he would not return to the tour until he felt 100 per cent fit.
"That could be in two weeks, that could be a little bit longer."
Read the original article on Eurosport: Nadal bagelled, still wins anyway