French Open finalist Zverev had cruised through to the semi-finals and not had his serve broken across all three of his group matches, but that was to change against an inspired Fritz.
Though he saved Fritz’s first break point opportunity, he could only bat a blistering forehand into the net on his second as the American took a 4-2 lead.
Flustered, Zverev took only a single point off Fritz’s serve for the remainder of the opening set.
After a Zverev love hold in the first game of the second, drama ensued on Fritz’s serve when the chair umpire ruled the ball had bounced twice before a swooping Zverev made contact.
The 27-year-old German requested a review which, after a lengthy wait greeted by jeers and whistles from the crowd, proved Zverev had reached the ball in time and the point was replayed.
Two games later, Zverev secured the break that would decide the second set as a powerful forehand while on the backfoot proved too much for Fritz to dink back over the net.
In the deciding set, just three points were dropped on serve across the opening four games before Fritz, who reached his first Grand Slam final at the US Open in September, handed his opponent triple break point with three successive errors off his racquet.
The American saved the first with an ace before forcing Zverev into two mis-hits and eventually holding.
But as the set continued on serve, the pressure mounted with both players knowing whoever got a break would likely win the match.
Zverev weathered a nervy game, saving three break points, before failing to convert two of his own at 5-5 after Fritz had let slip a 40-15 lead.
A love hold from the German forced the tie-break, but it was Fritz who took control from there, taking a point off Zverev at the first opportunity before a stunning cross-court forehand at match point ensured his Tour season would last one more day.
Later on Saturday, Britain’s Henry Patten and his Finnish partner Harri Heliovaara were knocked out of the doubles in a tight 7-6 (7-1) 7-6 (7-4) semi-final defeat by the top seeds, Croatia’s Mate Pavic and El Salvador’s Marcelo Arevalo.