Washington acquired Hagelin from the Los Angeles Kings on Thursday for a third-round pick in the 2019 NHL Draft and a conditional sixth-round pick in 2020.
The Capitals, winners of two straight and 6-2-1 in their past nine games, are second in the Metropolitan Division, two points behind the New York Islanders.
The Sabres have lost four in a row (0-3-1) and have been outscored 15-6 during the streak. They've scored two goals or fewer in five of their past six games. Buffalo trails the Carolina Hurricanes by six points for the second wild card into the Stanley Cup Playoffs from the Eastern Conference.