The meeting, which took place at the TD Garden arena in Boston, ended with a score of 5: 2 in favor of the hosts.
David Pastrnyak scored a hat-trick among the winners.
Charlie McAvoy and Taylor Hall also scored once.
Anthony Beauvillier and Adam Pelech scored at the Islanders.
Russian goalkeeper Ilya Sorokin saved 35 out of 39 shots.
The score in the series was 1: 0 in favor of Boston.
The next match will take place on June 1st.
Earlier it was reported that the NHL club Los Angeles announced the signing of a contract with Tkachev.