Strome, who signed one-year, $3.5 million contract on July 14, and Brown, who was acquired in a trade with the Ottawa Senators on July 13, were each making their debuts for Washington.
Bobby Nardella had two assists, and Charlie Lindgren started and made 13 saves in two periods for Washington. Zach Fucale allowed one goal on eight shots in the third.
Kevin Hayes scored for Philadelphia. Felix Sandstrom allowed two goals on 15 shots in two periods before being replaced by Samuel Ersson, who made 11 saves in relief.
Brown gave the Capitals a 1-0 lead at 4:23 of the second period, and Strome made it 2-0 with a power-play goal at 7:42.
Hayes cut it to 2-1 at 3:44 of the third period, but Strome scored at 16:20 off a pass from Brown for the 3-1 final.
