Strasburg (1-0) went seven innings allowing three hits and striking out three.
Washington managed just five hits off Miami pitching and only three of those came off Marlins' starter Ricky Nolasco (0-1), who struck out five and walked two over six innings.
However, Harper twice hit breaking balls from Nolasco for home runs. He hit a two-out home run in the first innings and led off the fourth with another shot into the right-field seats.
At 20 years of age, Harper is the youngest player to hit two home runs on an Opening Day game.
Swim Week Miami Beach 2014 [PHOTOS]