Cruz, who had been granted a wildcard into the ATP-250 event, upstaged Sebastian Gorzny to win their first-round match 1-6 7-6 (7-3) 6-4.
The rising star of Australian tennis survived a barrage of aces, 12 in all, from the American before advancing in a battle lasting over two hours.
Showing the trademarks of his famous father - former world No.1 Lleyton Hewitt - the 17-year-old had to dig deep after dropping the first set in rapid quick time.
He fought back to take a hard-fought second set in a tie-breaker before earning the crucial break in the ninth game of the third against the lucky loser.
"He played an amazing first set, I didn't really know what to expect," Hewitt said.
"Then I thought I handled the pressure well and came back playing some better tennis than the first set and it was a fun battle for sure."
Hewitt hit 11 of his 18 winners in the final set.
"I think this is a great first match to get into the tournament, play on these courts. It was my first time playing here so I feel like the longer the match was better preparation for the next match for me.
"I feel like I was competing really well. I wanted to win so I just stayed out here to try and get the win so that was probably what I was most happy about."
Last month Hewitt broke through for his maiden victory when he upset one-time world No.37 Marcos Giron in straight sets at the Mubadala Open in Washington.
He will be hoping for another giantkilling act when he next meets Britain's top player and tournament No.4 seed Arthur Fery in the round of 32.
Hewitt's victory was one of the shining lights for the Australian contingent, one week out from the US Open.
James Duckworth warmed up for his appearance at the final grand slam of the year with a 6-2 6-1 win over Quinn Vandecasteele.
Duckworth needed just 72 minutes to dispatch the 456th-ranked American qualifier and he will now take on Argentine sixth-seed Mariano Navone, ranked No.48.
Adam Walton, who made his US Open debut last year, is back at Flushing Meadows again and he beat Dutchman Jesper de Jong in straight sets.
Walton, who won 6-2 6-4, will next play third-seeded Peruvian Ignacio Buse.
They are joined in the second round by Rinky Hijikata, who had defeated wildcard Darwin Blanch 6-4 7-6 (7-2) the previous day.
Hijikata next faces Belgian fifth-seed Raphael Collignon.
There was also joy for Indian player Dhakshineswar Suresh, who dished out 17 aces on his way to upsetting Giron in straight sets.
Lucky loser Suresh beat the American 6-3 7-5, in an ominous sign for Giron ahead of the US Open.
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