Britain and Ireland took a 3-1 lead in the morning foursomes in the two-day amateur competition, but the Americans went ahead 4-3 when Peter Uihlein, Jordan Spieth and Harris English won the first three singles matches in the afternoon. After heavy rain, the 17-year-old Pugh, from Wales, started the rally.
"I've got a lot of confidence in these boys," Britain and Ireland captain Nigel Edwards said. "They're a great bunch of lads and they've proved it this afternoon. They've knuckled down and done the job."
Top-ranked Patrick Cantlay earned the last point for the Americans, beating Michael Stewart on Royal Aberdeen's Balgownie Course.
The competition will conclude Sunday with four foursomes and 10 singles matches.
There was a bit of controversy after the morning session, when Jack Senior used his brother, Joe, as his caddie in teaming up with fellow Englishman Andy Sullivan to beat American Kelly Kraft and Russell Henley.
Joe Senior is a professional golfer and is therefore not allowed to partake in the event, but organizers allowed the result to stand because the infraction wasn't brought to their attention until after the match.
Edwards called it "a bit of a mishap" and praised his U.S. captain Jim Holtgrieve for not making it an issue.
"We chatted about it. Jim was great about it," Edwards said. "It was a mistake, and I can assure you, from my point of view, that it was never intended. It was one of those things."
Senior then used a different caddie for the singles, losing to Spieth.
Holtgrieve said he never considered lodging a protest over the illegal caddie.
"When they approached me and told me about it, it was not an issue for me at all," he said. "That gentleman did not hit any golf shots. He did not affect the outcome of the match. Common sense says that it was the right thing for us to do."
Cantlay also earned a point for the United States in the alternate-shot matches, teaming with Chris Williams to beat Steven Brown and Stiggy Hodgson 5 and 3.
In singles, Uihlein topped Tom Lewis 2 and 1, Spieth edged Jack Senior 3 and 2, English beat Sullivan 2 and 1 and Cantlay topped Stewart 2 and 1.
For Britain and Ireland, Pugh beat Patrick Rodgers 2 and 1, Brown topped Henley 1-up, Byrne stopped Nathan Smith 2 and 1 and Cutler edged Kraft 2 and 1.
The United States has won three straight times to take a 34-7-1 series lead.