As the opening ceremony began, Ms Kim and Mr Moon exchanged a historic handshake and spoke briefly, smiling broadly throughout. It is not known what they said.
Ms Kim’s arrival was broadcast live on South Korean television.
Looking confident and relaxed, she had a brief meeting with government officials, including Unification Minister Cho Myoung-gyon, before she was whisked away in a black limousine to catch the high-speed train to Pyeongchang.
Ms Kim, an increasingly prominent figure among the North Korean leadership, will spend three days in the South. She is expected to sit down for lunch with Mr Moon at the presidential Blue House in Seoul on Saturday.
Mr Pence meanwhile, will use his appearance at the games to call on the international community to get tougher on North Korea’s nuclear ambitions.
He will also warn against falling for the glossy image of the two Koreas as they march under one flag at the Games.
Ahead of the opening ceremony, Mr Pence made a brief appearance at a dinner for visiting foreign dignitaries, which was also attended by Kim Yong-nam, the highest-ranking North Korean official to travel to the South.
A White House official said Mr Pence did not interact with Ms Kim or Kim Yong-nam
UN secretary-general Antonio Guterres, who sat near Mr Kim at the dinner, had a brief exchange with him and “reiterated his expectation and hope that all parties will use dialogue to achieve the denuclearisation of the Korean Peninsula,” UN deputy spokesman Farhan Haq said.
Guterres was also in “the same general area” as a number of other North Korean officials including Ms Kim “but they were never in any personal contact with each other,” Mr Haq said.
An encounter between the pair has been mooted, but Mr Kim but said the US had not requested a meeting.
Speaking to NBC’s Nightly News, in an interview aired on Friday night, Mr Pence, vowed that the US would protect itself from North Korean nuclear threats by taking whatever “action is necessary to defend our homeland”.
Mr Kim is leading the North Korean delegation to its neighbour, which Ms Kim is technically just a member of.
However, at the age of 30, she widely seen as the most powerful woman in North Korea. She has been rapidly rising within the country’s power structure and is believed to be in charge of shaping her brother’s public persona.
This is her first high-profile international appearance at centre stage.
For security reasons, few details of Ms Kim’s three-day itinerary have been made public.
After arriving on Mr Kim’s personal jet at the South’s ultramodern Incheon International Airport – the North’s flagship airline is subject to sanctions – she travelled to Pyeongchang, where the North and South Korean athletes marched together behind a blue-and-white “unification” flag during the opening ceremony.
Her brother, North Korea’s leader, has not set foot outside of his homeland or met a single head of state since he assumed power upon the death of his father, Kim Jong-il, in late 2011.
Tensions between his country, its near neighbours and the US have ratcheted up over the last year after North Korea conducted a series of missile tests.
In September, the secretive communist state also claimed it had tested a powerful hydrogen bomb that could be loaded on to an intercontinental ballistic missile – a claim that was later disputed by experts.
The two Koreas, which remain technically at war, have cycled through countless periods of chill and thaw since their division 70 years ago.
North Korea boycotted the 1988 Summer Olympics in Seoul, the year after it blew up a South Korean commercial airliner.
But a spirit of unity is being promoted at the current games.
The first match featuring the joint North-South women’s ice hockey team will also be held over the weekend, when they take on Switzerland.
The North has also sent a cheering squad made up of several hundred women, an orchestra with singers and dancers and a demonstration taekwondo team that will perform in Seoul and at places near the Olympic venues.
Security for anything involving the North Koreans has been exceptionally tight.
A small but persistent group of right-wing protesters has shown up at several venues to burn North Korean flags and tear up portraits of Ms Kim’s brother.
The group is fringe, but their demonstrations have generated irate reactions in North Korea’s state-run media and could potentially spin out into a major incident if they ever manage to get closer to the North Koreans themselves — or especially Ms Kim and her entourage.
Additional reporting by agencies