The Capitals now are 7-1-0 in their past eight games and improved their lead in the Metropolitan Division to five points over idle Pittsburgh and six over Columbus, who broke a 10-game winning streak with a loss on Saturday.
Washington and Pittsburgh each have seven games left in the season, and Columbus has six remaining.
Wilson had not scored a goal in his last 10 games but got two in a three-goal first period. Kuznetsov scored a goal in the first and another early in the third.
Backstrom assisted on each of Washington's three first-period goals.
Goalie Philipp Grubauer made 17 saves in the victory.
Montreal scored the game's first goal on an Alex Galchenyuk shot 8:35 into the game. The Canadiens appeared to make it 2-0 just over a minute later but the goal was thrown out (offsides) after Washington challenged the play.
The Capitals took over after that, posting three goals in a seven-minute stretch.
Kuznetsov, who returned the lineup after missing three games with an upper-body injury, tied the game on a power-play goal with 8:49 remaining in the period.
Wilson then scored back-to-back goals that gave Washington a 3-1 lead. The big right-winger has thrived when playing on the first line and notched two quick goals. The first, which snapped the tie, came after goalie Carey Price's weak pass trickled away from a teammate and to Backstrom. He quickly fed Wilson, who beat Price from the right circle with 5:11 left.
Backstrom set up Wilson once more with 1:49 remaining, making a beautiful no-look pass to his left, and the right winger buried it from the high slot.
Jay Beagle then made it 4-1 early in the second period before Charles Hudon scored for Montreal just two seconds before intermission.
Kuznetsov --thanks to Backstrom's fourth primary assist, this also on the power play-- and T.J. Oshie each posted a goal in the third for a 6-2 lead.
Hudon added his second goal, and Brendan Gallagher added a late-power play marker for the 6-4 final.
--Field Level Media
Washington | Montreal | |
Nicklas Backstrom 4 | Points | Charles Hudon 2 |
Evgeny Kuznetsov 2 | Goals | Charles Hudon 2 |
Nicklas Backstrom 4 | Assists | Logan Shaw 2 |
Evgeny Kuznetsov 2 | Power Play Goals | Brendan Gallagher 1 |
N/A | Short Handed Goals | N/A |
Philipp Grubauer .810 | Save Percentage | Carey Price .800 |
Philipp Grubauer 17 | Saves | Carey Price 24 |
Team | Shots | Goals | Power Play | Penalty Kill | Penalty Mins | Face Offs Won |
Washington | 30 | 6 | 2-3 | 2-3 | 6 | 39 |
Montreal | 21 | 4 | 1-3 | 1-3 | 6 | 29 |