Nadal began the event 1000 ranking points behind his fellow Spaniard and world number one Carlos Alcaraz, who is missing the tournament through injury, but now will have to win the title to overtake him.
His more immediate aim will be to raise his level in his second group match against Felix Auger-Aliassime after an error-strewn performance in a 7-6 (3) 6-1 loss to American Fritz.
The first set was high quality but Nadal, who also lost his opening match at the Paris Masters last week and has not tasted victory since the third round of the US Open more than two months ago, faded badly in the second.
It was a fine performance from Fritz, though, with the 25-year-old claiming a second victory of the season over Nadal after also beating him in the final in Indian Wells in the spring.
Nadal, who has been spending time at home with his new-born son, said: "I don't think I was getting in the right positions in the first set. I think that my serve worked well, then he was hitting the ball very strong.
"I need more matches to play at this kind of level, even if I am practising well, much better than how I am competing, without a doubt. That's normal.
"It's not the ideal tournament and probably part of the season to come back after a couple of months without being on the tour because you don't have time to get confidence.
"In this tournament I still have a chance. But of course I'm not happy about the beginning. That first match was very important for me."
He will next face third seed Casper Ruud, who played his best match since losing his second grand slam final of the year in New York to beat Auger-Aliassime 7-6 (4) 6-4.
Canadian Auger-Aliassime earned his first visit to the season-ending event thanks to a run of 16 straight victories and three consecutive ATP Tour titles in October and early November.
But, in a contest largely dominated by serve, he was unable to find the same form and a single break in the seventh game of the second set proved enough for Ruud.
Three British players are competing in the doubles event and two were victorious on Sunday.
Lloyd Glasspool and Finn Harri Heliovaara made an excellent debut, defeating French Open champions Marcelo Arevalo and Jean-Julien Rojer 7-5 7-6 (3).
US Open winners Joe Salisbury and American Rajeev Ram missed two match points in the second set against Marcel Granollers and Horacio Zeballos but came out on top of a tense deciding tie-break to win 6-3 6-7 (8) (10-8).
Neal Skupski and Dutchman Wesley Koolhof, who are the top seeds, begin their campaign on Monday afternoon against Australian Open champions Nick Kyrgios and Thanasi Kokkinakis.
Also on Monday, Novak Djokovic plays in the evening against Stefanos Tsitsipas, who also has a chance to overtake Alcaraz, while Russian duo Daniil Medvedev and Andrey Rublev face off.