7-magnitude tremor also left hundreds more injured in the Turkish resort of Bodrum, just about 20 kilometres across the sea from Kos.
“Given the amount of people outside at the time, having only two victims is a miracle,” deputy Kos mayor David Yerasklis told Kathimerini daily.
The undersea quake struck at 1:31 am Friday (2231 GMT Thursday) between Kos and Bodrum.
At the time, tourists in both places were out enjoying the nightlife.
0:00 Kos earthquake: residents, tourists assess the damage Share Kos earthquake: residents, tourists assess the damage
On Kos, a wall collapsed on people in the yard of a nightclub, killing a 22-year-old Swede and a 39-year-old Turk.
Another 120 people were hurt, seven of them seriously, while some 360 people were injured in Bodrum — many after jumping out of windows.
The badly injured on Kos were flown to hospitals in Athens and Crete, including two men from Sweden and Norway who are in critical condition.
The Swede lost his lower leg, and doctors are struggling to save his other leg. The Norwegian has serious head injuries.
Kos is one of Greece’s top travel destinations, and particularly popular with British and Scandinavian tourists.
Government officials and expert divers on Saturday were inspecting the harbour, which was cracked asunder by the tremor and has been declared unsafe for use.
But the rest of island’s infrastructure is mostly intact, they stress.
Ferries have been rerouted to the smaller port town of Kefalos in west Kos until repairs are made.
Some residents spent the night outdoors, setting up tents in parks and squares, but officials noted that the majority of hotels were unaffected by the quake.
At Kos airport, delays were noted for a second straight day with over 50 outgoing flights scheduled. Over a dozen flights had landed by mid-morning.
“There is no problem at the hotels, the tourists have dealt calmly with developments,” Constantina Svynou, head of the local hotelier association, told Ta Nea daily.
Some areas of the port town were still without water, however.
No injuries were reported among the 800 migrants and refugees housed on the island, which is one of the main gateways into Europe for people fleeing war and poverty.
But asylum procedures have been curtailed until at least Monday as the quake damaged passport inspection facilities at the harbour.
Many archaeological and medieval monuments — including the medieval Knights of St John fortifications near where the deaths occurred — have also been closed until further notice.
Turkey and Greece sit on significant fault lines and have regularly been hit by earthquakes in recent years.
This year alone, Turkey’s western Aegean coast was hit by several significant earthquakes.
In June, a 6.3-magnitude earthquake gutted a village on the Greek island of Lesbos, killing a woman and leaving more than 15 injured.