Saku Koivu and Sheldon Souray also scored and Guillaume Latendresse had two assists for Montreal, which has won six of seven games and three in a row against Washington.
Canadiens goaltender Cristobal Huet came within 2:56 of his 14th career shutout, which Alexander Semin ruined by knocking in his own rebound on a power play.
Washington has lost two straight and four of five games.
The Capitals wasted three power plays and a 14-7 shots advantage in the first period, and Montreal grabbed a 2-0 lead on the first goals of the year by Dandenault, who broke a 27-game goal drought, and Downey, his first since April 17, 2006.
Dandenault scored on a run to the right post, converting a cross-crease pass from Latendresse at 12:36. Downey made a dash down the slot, redirecting a pass from Radek Bonk by Olaf Kolzig, who blocked the puck only to have it bounce high, off his right shoulder and in.
Koivu tipped Souray's shot past a screened Kolzig for a power-play goal with 5:14 left in the third for a 3-0 lead. Souray answered Semin's goal with a short-handed empty-net goal with 45 seconds remaining.
Notes: There was a moment of silence before the game to honour former U.S. President Gerald Ford, who died Tuesday night. Ford was president when the Capitals entered the NHL as an expansion team for the 1974-75 season . . . Montreal was the last Eastern Conference team the Capitals hadn't played . . . Montreal C Steve Begin (ribs) missed his seventh straight game . . . Washington played without D Shaone Morrisonn (undisclosed illness) and D Bryan Muir (broken foot).