Zverev surrendered the first set to Fritz with four unforced errors in a row on Saturday in his final service game.
The German quickly hit back with a break in the second set, but then lost his way as Fritz recovered and then clinched the match with another break after a forehand winner.
Carlos Alcaraz earlier blitzed Ben Shelton 6-4 6-4 to pull Europe level at 4-4.
Alcaraz, the French Open and Wimbledon champion took just one hour and 43 minutes on the indoor Berlin hard-court to dispatch the American world no.17.
Spaniard Alcaraz said: "I tried to get in as many returns as possible so I could play long rallies. Playing against him you never know which serve he's going to give you. His serve is crazy."
American Frances Tiafoe opened the day's play by coming from behind to beat Daniil Medvedev 3-6, 6-4, 7-6 (10-5).
Russian Medvedev cruised to the first set, dominating especially on his second serve, but Tiafoe hit back by breaking in the first game of the second set.
The clash went to a match tie-break and Tiafoe raced to a 10-5 triumph.
"I respect everyone, but I'm just not fearing anyone at the moment," said Tiafoe.
"Honestly, I just started having fun. I started to find my rhythm . midway in the second and in the tie-break, I felt like I was Roger Federer."
With a doubles match completing the day's action in the evening session, the winning team need to reach 13 points for victory.
Two points are awarded for wins on Saturday compared to one point on Friday. Sunday's wins are worth three.
11°C