Drew Stafford scored twice and Ryan Miller dominated in goal with 44 saves to give Buffalo their biggest win of the season, and fifth straight, putting them in the driver's seat to reach the post-season.
"We've been in this (playoff) mode for a while, where every game has been a must-win for us," Stafford said.
"Obviously with this game, them being right there with us in the standings, the stakes are a little bit higher, but we're not done yet."
After sitting bottom of the conference two months ago, Buffalo's (38-29-10) dramatic comeback now has them two points in front of Washington (38-31-8) in the race for the eighth seed with just five games each remaining.
Buffalo blew past the Capitals with a fast start. Cody McCormick and Stafford scored in the first period and Thomas Vanek put them further ahead early in the second.
Alexander Semin netted the lone Washington goal in the second, where Buffalo's Jason Pominville also capitalised before Stafford hammered in a final nail midway through the third.
The Capitals, having won four consecutive Southeast Division titles, have lost three of four and suddenly find themselves on the outside looking in on the playoff picture.
One factor working in Washington's favour, however, is they hold the tiebreaker over the Sabres with more non-shootout victories.
"You got to forget about (the loss) now, it's done," Capitals coach Dale Hunter said. "We need to win in Boston (on Thursday)."
Sabres defenseman Christian Ehrhoff left in the first period with a left leg injury and will be evaluated Wednesday.