The former sung the South Korean national anthem with 25 elementary school children, while the latter performed its 2017 hit "Shangri-La", which features Korean traditional aesthetics.
Moon joined Kim Yo Jong and other North Korean supporters Saturday in cheering for the team against Switzerland. Before now, she had been seen mainly in photos, but often in the background, as her brother took center stage. Just a few years younger than her brother, she is believed to be his closest confidant and is a senior cadre in North Korea's ruling party.
It would be the first summit in more than a decade between Korean leaders.
Ms Kim, who is said to be very close to her brother, was promoted to the powerful politburo previous year.
Kim Jong-il, Kim's father, had met with two South Korean presidents in Pyongyang, the North Korean capital, before his death in 2011: with President Kim Dae-jung in 2000, and with President Roh Moo-hyun in 2007.
She and Kim Yong Nam, the North's 90-year-old nominal head of state, were seated behind Moon and his wife, while Mr Pence and his wife were seated beside the Moons and Japanese Prime Minister Shinzo Abe.
Pence told reporters that the two leaders "spoke as friends" during his visit to South Korea, and their discussions including the meeting between Moon and the North Korean delegation, led by Kim Jong Un's sister, Kim Yo Jong.
The recent detente, anchored by South Korea's hosting of the Winter Olympic Games that began on Friday, came despite an acceleration in the North's weapons programs a year ago and pressure from Seoul's allies in Washington. After the game, the entire group walked around to the Koreans' bench to greet them and pose for photos.
Diplomatically, Kim Jon Un's move delegating his sibling to attend the Winter Olympics as part of a "charm offensive" is aimed at winning over South Korea and drawing it away from the US's sphere of influence. It's anyone's guess as to when we might learn what's behind the facade.