Alcaraz then levelled proceedings at 4-4 with his win, but Taylor Fritz claimed another big victory over Alexander Zverev, beating the German 6-4 7-5 in Berlin to move Team World 6-4 in front.
In the final match of the second day, Shelton and Alejandro Tabilo comfortably defeated Casper Ruud and Stefanos Tsitsipas 6-1 6-2 in doubles for an 8-4 advantage.
Match wins count for three points on Sunday, with 13 needed for overall victory.
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“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.
Alcaraz also hit out at the packed tennis calendar in the aftermath of his display.
The Spaniard said the sport’s governing bodies are going to “kill us in some way” because of the physical demands exerted on players.
Britain’s Jack Draper called the schedule “mental” after heading from the US Open to Manchester to play in the Davis Cup for Great Britain last week.
Alcaraz told a press conference: “Probably during the next few years it’s going to be even more mandatory tournaments. Probably they are going to kill us in some way.
“Right now there are a lot of injured (players), because of the balls, because of the calendar, a lot of things. Probably at some point a lot of players are going to miss a lot of tournaments because of that.”
Team World’s Frances Tiafoe had earlier come back from a set down to defeat Daniil Medvedev in the opening match of the day at the Uber Arena.
What’s coming up on Sky Sports Tennis in September?
- Korea Open – WTA 500 (September 16-22)
- Thailand Open – WTA 250 (September 16-22)
- Chengdu Open – ATP 250 (September 17-24)
- Hangzhou Open – ATP 250 (September 18-24)
- Japan Open – ATP 500 (September 25-October 1)
- China Open – ATP 500 (September 26-October 2)
- China Open – WTA 1000 (September 25-October 6 – with Emma Raducanu in action)