But the news was much better for world No.3 Coco Gauff, who was at her ruthless best in a 6-1 6-1 demolition of Solana Sierra in Perth on Saturday night before teaming up with Christian Harrison to guide the US to a 6-4 6-1 win in the deciding mixed doubles.
Fritz - who has been battling tendonitis in recent months - was withdrawn from the doubles to protect his knee.
The 28-year-old was well on track to win his men's singles match after taking the first set and going up 2-0 in the second.
But world No.45 Baez had other ideas, unleashing his trademark fighting spirit to turn the match on its head.
Baez took the second set in 66 minutes and snared an early break in the third on the way to his 4-6 7-5 6-4 victory in two hours and 33 minutes.
Fritz's frustrations boiled over after losing the final point, the American snapping his racquet over his thigh.
After shaking hands with his opponent, a downcast Fritz then gave the broken racquet to a kid in the crowd before leaving the court.
On the eve of the United Cup, Fritz revealed he was still dealing with "pretty serious tendonitis" that had plagued him at the tail end of last year.
The American knows he will have to deal with the knee issue at this year's Australian Open, and said after Saturday night's singles loss that a stint on the sidelines is on the cards if it doesn't get better in the next few months.
"I spent the majority - pretty much the entirety - of the off season trying to rehab my knee tendinopathy," Fritz said after the upset loss.
"But that's a thing that takes months and months to get better.
"So you know, I didn't get to play a lot of points because I'm trying not to push it too hard.
"It's just going to be a struggle trying to get the reps in and get the points and matches in to start feeling like I'm comfortable while juggling that with still managing my knee pain.
"I'm going to try to play through and keep doing the rehab while travelling.
"But if that doesn't work in a couple of months, then I am going to just have to full stop and fix it."
Baez had lost all five of his previous meetings with Fritz, and he was over the moon to finally take down his highly-fancied opponent.
"Wow, I'm so happy right now," Baez said.
"We are searching this feeling for many years. Taylor beat me many, many times, so I'm happy to take one."
The women's clash was all one-way traffic as two-time grand slam champion Gauff wrapped up victory against the error-riddled Sierra in 57 minutes.
"I'm really happy. There was a little bit of pressure," Gauff said.
"I feel like I can play even better too, which is even more exciting."
The defending champions US will lock in a quarter-final berth if they can beat Spain on Monday.
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