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The Penguins scored two quick goals early in the second period before exploding in the third to take a commanding 3-1 series lead.
Chris Kunitz and Jarome Iginla scored 40 seconds apart and Iginla and James Neal each scored twice to lead the Penguins.
After the game, Senators captain Daniel Alfredsson was dejected by his team's performance. He was honest and struggled to find the positives when asked if the team could win three games in a row to win the series.
"Probably not," he said, "Their depth and power play right now, it doesn't look too good [for us]."
Head coach Paul MacLean pointed to the stats sheet after the game when asked how Wednesday's game went for Ottawa.
"It's seven to three. See you in Pittsburgh," MacLean said in brief comments to reporters without taking questions. "We're going to Pittsburgh and we're coming to play."
Sens' Anderson pulled for 2nd time in 3 games
Craig Anderson had a great first period to lead the Senators to a 2-1 lead but the Penguins kept coming and chased Anderson from the net.
The Senators scored first, and led, for the first time in the series. Just over two minutes into the game, Milan Michalek showed no ill effects from his bad knee, speeding between the Penguins' defence to score on a short-handed breakaway.
Then after James Neal tied it up later in the period, Kyle Turris restored the Senators lead when he dove to tap in a rebound.
The Penguins dominated that first period, though, and unlike Game 3 they were able to persevere and put more than one puck past the Senators netminder.
They also scored once on the power play and once shorthanded in the third period to sink the Senators. Sidney Crosby scored the sixth goal to knock Anderson from the net, the second time the Penguins captain has done so in three games.
Sens' Alfredsson scores 100th playoff point
Ottawa will look to salvage their season in Game 5 on Friday night in Pittsburgh.
One positive for Ottawa came on their third goal, scored by Alfredsson after they were already down by five goals. It was the captain's 100th career playoff point.
The Sens inserted 21-year-old winger Mark Stone for Game 4, looking for magic similar to last year's first-round series against the New York Rangers, but it was not the case Wednesday night.
Penguins head coach Dan Bylsma also made two lineup changes, replacing an injured Brenden Morrow and Tanner Glass with centre Jussi Jokinen and winger Beau Bennett. The new fourth line was effective for the Penguins.