Ovechkin opened the scoring at 8:10 of the first period with Washington's first power-play goal of the series. Mike Knuble tied it at 2 with the Capitals' second shorthanded goal in two games with 6.3 seconds left in the second.
Ovechkin added his second of the game and fourth in three games to put Washington up 3-2. Jason Chimera made it 4-2 just 52 seconds later.
The Capitals got empty-net goals from Knuble with 2:27 left and Nicklas Backstrom with 10.1 seconds remaining.
Semyon Varlamov made 36 saves to win his third in a row for Washington, which regained home-ice advantage in the quarterfinal series with a 5-1 victory in Game 3 on Monday night.
Carey Price stopped 32 shots in his first start of the series for Montreal. Price, who replaced Jaroslav Halak in the second period Monday, was penalized for unsportsmanlike conduct when he fired a puck toward the Capitals players celebrating Chimera's goal.
Price drew another unsportsmanlike conduct minor following Backstrom's goal.
Michael Cammalleri, Brian Gionta and Dominic Moore scored for Montreal, which outshot Washington 21-9 in the second after holding a 12-9 edge in the first.
Game 5 is Friday night in Washington.
The Capitals fell to 0-for-15 with the man advantage in the series when they failed to score during their first opportunity after Tomas Plekanec was sent off for interference 48 seconds in.
Ovechkin brought the power-play skid to an end when he drove a shot past Price to extend his goal streak to three games and put Washington up 1-0.
Cammalleri drew Montreal even 1:12 later with his second goal. Cammalleri put a backhand of a rebound of Glen Metropolit's shot in at 9:12 after the Montreal center came out from behind the net and tried to tuck his own backhand past Varlamov.
Gionta drew a roar from the capacity crowd of 21,273 when he scored a power-play goal from the left edge of the crease 15:42 into the second to put Montreal up 2-1.
Knuble silenced the crowd when he put Boyd Gordon's pass beyond Price with 6.3 seconds left in the second.
Notes
The 21 shots allowed by the Capitals in the second period matched a team playoff record for shots by an opponent in a period set by Philadelphia on April 21, 2008. … Canadiens D Jaroslav Spacek missed the game because of an unspecified injury. Ryan O'Byrne took his spot in the lineup.