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Fritz went one better than Draper at Flushing Meadows, reaching the final before losing to Jannik Sinner.
But he was edged out on this occasion in an engrossing match.
A stunning forehand winner after chasing down a Fritz smashed helped Draper sneak the first set on a tie-break but the second set threatened to swing towards the world number six.
At 3-2, Draper failed to take any of six break points in a marathon Fritz service game that included 10 deuces. The American broke to love in the next game en route to taking the set and levelling the match.
But Draper, who only left the court in Vienna on Sunday afternoon and beat Czech Jiri Lehecka on Tuesday, resisted the swing in momentum and dug deep as his energy levels seemed to waver.
He used his powerful left-handed serve well throughout and capitalised on a wild double fault by Fritz at the end of a tight deciding set to take the contest on his first match point.
“It is the end of season – a lot of people are hurting, not just myself,” added Draper.
“I will keep fighting for every point no matter how I am feeling.”
Earlier, Russian fifth seed Daniil Medvedev was beaten 6-4 2-6 7-6 (7-4) by Australian Alexei Popyrin.
But third seed Alexander Zverev and eighth seed Grigor Dimitrov both progressed with victories against Tallon Griekspoor and Tomas Martin Etcheverry respectively.
In the final match of the day, Frenchman Arthur Cazaux – a lucky loser ranked 85th in the world – stunned American world number 19 Ben Shelton 6-3 7-6 (7-4) in front of a raucous home crowd.