The Internationals led 4-1 after Thursday’s first fourball session and were ahead in all five foursomes matches Friday before the defending champion rallied to end 6½-3½ at Royal Melbourne.
“At one point it looked pretty bleak, but the guys turned it around. They played phenomenal coming in,” debutant captain Woods told a joint news conference with International counterpart Ernie Els.
Saturday features a further eight matches before all 12 players on each team go head-to-head in singles Sunday. The International team is looking to avoid an eighth straight defeat in the biennial contest, similar to the Ryder Cup between USA and Europe.
Els’ International team picked up where it left off and at one point a clean sweep was on the cards in the alternate-shot foursomes session.
South African Louis Oosthuizen and home favorite Adam Scott beat Dustin Johnson and Matt Kuchar 3&2 in the first match, but Patrick Cantlay and Xander Schauffele found a way to beat Canada’s Adam Hadwin and Chile’s Joaquin Niemann 1 up to stay in touch.
However, the Internationals edged ahead again when Mexico’s Abraham Ancer and Australian Marc Leishman beat Patrick Reed and Webb Simpson 3&2.
Masters champion Woods, who picked himself as a wildcard on the team, partnered Justin Thomas for the second day to beat South Korea’s An Byeong-hun and Japan’s Hideki Matsuyama 1 up to give the US some hope.
And in the final match, Rickie Fowler and Gary Woodland battled to a half with South Korea’s Im Sung-jae and Australian Cameron Smith.
“It was important for us to end the way we did and it totally changed the last hour,” added Woods, the 15-time major champion.
“The energy has been there. These guys are all young and extremely excited about being part of this team.”
The USA has won 10 of the previous 12 events since the Presidents Cup began in 1994, but Els, one of Woods’ main adversaries in their heydays, is sensing an opportunity.
“Look at the record we’ve had in the foursomes the last 25 years and for us to come out 2½-2½ in the session is like a win for us,” he said.
“We would have taken that at the start of the day.”
Four-time major champion Els added: “It’s perspective, isn’t it? I’ve got to look at where we are. It’s easy to just look at where we could have been, because it was looking really unbelievable.
“But we’re in a very good position.”