However, despite losing the first set 6-3 after losing his serve in the second game, Goldstein won the next 7-5 before triumphing 10-7 in the super tie-break.
"Ken's a good player and it was one heck of a match," said Goldstein.
"He came out firing and never looked like losing the first set. He played really well, but I found some form and played much better.
"The tie-break was good fun, but I returned well enough to win and I felt that made a big difference.
"I've got to qualify for Wimbledon next week, so I'm really grateful to have got this practice.
"I'm hoping to do well this week. I enjoy playing in Liverpool."
RESULTS: Men's Singles: Group C: Stian Buretti (Nor) bt Bobby Reynolds (USA) 7-5 1-6 12-10 (super tie-break). Group B: Paul Goldstein (USA) bt Ken Skupski (England) 3-6, 7-5, 10-7 (super tie-break). Mixed Doubles: Martin Navratilova & Jan-Michael Gambill bt Sam Smith & Ivan Ljubicic 6-2 6-7 10-6 (super tie-break)
TODAY: Centre Court, 11am. ATP Group B: Jan-Michael Gambill v Ken Skupski. 12.30pm ATP Group A: Novak Djokovic v Jan-Frode Andersen. 2pm Maro Development Youth Final. 3.30pm Mixed Doubles: Martina Navratilova & Robert Kendrick v Caro Borgersen & J-M Gambill. 5pm Legends Doubles: Mansour Bahrami & Henri Leconte v Ilie Nastase & Peter McNamara. 6.30pm ATP Group A: Ivan Ljubicic v Bobby Reynolds.
