Standing 6 foot 7 inches (201 cm) tall, Eubanks would look more at home on an NBA court than Court One at Wimbledon but he arrived at the All England Club after breaking into the top 50 with his first ATP title at the Mallorca Open last week.
In a match between two players who came through the American college system, the wiry Eubanks struck 63 winners and fired down 21 aces that screamed past 12th seed Norrie, who reached the Wimbledon semi-finals last year.
No matter how many rackets Norrie requested be restrung, he could do little to nullify Eubanks's power.
The American player received a standing ovation from the crowd despite knocking out one of Britain's biggest hopes.
"There's tons of really good tennis players who play professional tennis who never get the chance to play the number one Brit at Wimbledon in an atmosphere like this," Eubanks said.
"It didn't even matter how many people were for me or against me, this is something I'll never forget for the rest of my life."
For a player making his Wimbledon debut, Eubanks showed no signs of nerves as Norrie failed to win a point off the American's serve until the seventh game of the match.
Rallies were also in short supply as Eubanks mixed power and finesse with his serve and volley game to baffle Norrie to take the opening set.
Errors crept into his game in the second set, however, which allowed Norrie to race into a 3-0 lead and the Briton, egged on by a vocal home crowd, levelled the match.
Eubanks's power game seemed unsustainable, but the American broke early in the third set and clinched it.
His long strides allowed him to cover the court quickly and the self-confessed Roger Federer fan won 23 points at the net, winning the fourth set tiebreak with a deft volley.
"I watched a lot of Federer growing up. He's the guy that even to this day I still go back and try to find some of his old matches and just try to pick little things up," Eubanks added.
"I know he's a far better mover than I am... But I try my best to just take little bits of various players and to implement them into my game and try to create a style of my own."
