The duo had to return on Monday morning to decide the winner in Williamsburg, Virginia after they could not be separated by eight play-off holes on the par-4 18th before the failing light halted play on Sunday night.
They finally decided the winner on the par-4 16th.
"I know winning is always tough - but not this tough," Shin said.
The previous longest play-off in LPGA history was won by Cristie Kerr against Seol-An Jeon in the 2004 Takefuji Classic, which lasted seven holes.
They even had to reschedule their flights to England ahead of the British Open.
"I don't think I said anything to [her caddie] Colin [Cann] until I think the seventh play-off hole," Creamer said. "I said, 'I don't think we're going to make our charter.'
"He said, 'No, I don't think so. It leaves in 20 minutes or something.' It wasn't like we were thinking British, British, British, but yeah, we want to get there, too."
Creamer, who started the round with a two-shot lead over Shin, bogeyed the 18th in regulation play to go to the play-off.
Karine Icher and Danielle Kang finished tied for third, two strokes back on 14-under, with Angela Stanford and Catriona Matthew on 13-under and the Miyazatos Ai and Mika - who are not related - on 12-under.