The 29-year-old Barkov became last season the first Finnish team captain to lift the Stanley Cup trophy when his Florida won the final series over Edmonton.
When Barkov brought the trophy to Tampere last summer, 15,000 spectators came to Nokia Arena.
When he now brought his entire team to Tampere and the Global Series with double matches against Dallas, he got an initial dream evening.
Barkov completely dominated the ice, was credited with his first of three assists on Evan Rodrigues' leading goal already after 28 seconds and scored himself 2-0 after just over seven minutes.
In total, there were seven Finnish players on the ice, four in Florida and three in Dallas, and Anton Lundell was also credited as one of Florida's goal scorers.
Esa Lindell scored one of Dallas' goals.
Three Swedes were on the ice, and Florida's star defender Gustav Forsling was credited with an assist.
The teams will meet again at Nokia Arena on Saturday.
