Dan Vladar made 25 saves for Boston (21-12-6), which allowed a season high in goals and lost for the second time in as many days following a 3-2 loss at the Philadelphia Flyers on Saturday.
"It's really important (to look forward), especially in a season like this where you're playing every other day or back-to-back," Bruins captain Patrice Bergeron said. "That's definitely something you have to have, especially after a game like today. Obviously, there's no excuses and it was a very, very poor showing. But that being said, we have to look forward and if there's video tomorrow or the next day, look at it and be ready for Buffalo (on Tuesday)."
Oshie scored a power-play goal to give Washington a 1-0 lead at 7:33 of the first period, and Eller scored 16 seconds later to make it 2-0.
Sheary extended the lead to 3-0 at 9:42 before scoring his second goal on the power play at 4:41 of the second period to make it 4-0.