Connor made it 2-0 at 7:20 of the third period.
"Every game gets a little tough here, especially when you're playing teams that are scratching and clawing for points, as we are," Capitals coach Todd Reirden said. "Tonight, we get into a situation where their top line (Scheifele, Connor and Blake Wheeler) is one of the top combinations in the League, and they had [the] last (line) change and we get into some unfavorable matchups, and they were able to score the second goal."
Scheifele scored into an empty net with 1:28 remaining for the 3-0 final.
It was the second half of a home-and-home; Washington won 4-3 in the shootout on Tuesday.