The show was the final set-piece of the North Korean delegation's landmark visit, the diplomatic highlight of the Olympics-driven rapprochement between the two halves of the peninsula.
They have shared kimchi and soju, sat in the same box at the Pyeongchang Winter Olympic Games opening ceremony and cheered a unified women's ice hockey team.
Kim invited Moon to a summit in the North, an offer extended by his sister and special envoy Kim Yo-jong.
Pictures showed Yo-jong seated between Moon and the North's ceremonial head of state Kim Yong-nam, who is officially leading the North's delegation.
The show was given by some 140 members of Pyongyang's Samjiyon Orchestra as part of a cross-border deal in which the North sent hundreds of athletes, cheerleaders and others to the Games in the South.
At a dinner beforehand with senior Seoul officials, Yo-jong said she found the two Koreas still had much in common despite decades of separation.
Before flying south, she said, she had expected "things would be very different and unfamiliar," according to a statement from Moon's office.
"But it turned out that there were many things similar and in common," she went on. "I hope that the day we become one will be brought forward."
The North's presence has dominated the headlines in the early days of the Games, with all eyes turning to Swiss-educated Kim Yo-jong, believed to be 30, who is among her brother's closest confidantes.
Sunday's concert - the orchestra's second and final show - was expected to feature South Korean pop songs as well as North Korean music, with the diplomatic delegation due to fly home afterwards.
Civilian contact is strictly banned between the two Koreas, which have been divided by the heavily fortified Demilitarized Zone since the 1950-53 Korean War ended with an armistice instead of a peace treaty.
Moon has long sought engagement with the North to bring it to the negotiating table, and for months has promoted Pyeongchang as a "peace Olympic Games."