Alcaraz, who has already claimed titles at this year’s French Open and Wimbledon, demonstrated remarkable composure during critical moments, saving all five break points he encountered. He broke Shelton’s formidable left-handed serve once in each set to secure the win.
"First of all, I am really happy to be part of Team Europe for the first time, and am trying to be the best player that I can be to help my team," world no. 3 Alcaraz said.
"I played against a player that is really powerful, a really tough one, I’m really happy because I played a really solid match since the beginning."
Team World's Frances Tiafoe had earlier come back from a set down to defeat Daniil Medvedev and the two sides were tied at 4-4 going into the Saturday night session at Berlin's Uber Arena.
Germany's Alexander Zverev and American Taylor Fritz were next up to face each other before a doubles match concludes the day.