Brady Tkachuk, Tim Stutzle, Drake Batherson and Jake Sanderson also scored to help Ottawa win its second straight after a two-game skid. Cam Talbot finished with 22 saves.
Senators coach D.J. Smith credited Tkachuk's physical play as a key to the win.
''He came to play,'' Smith said. ''He's played a lot of games, a lot of minutes against everyone's top defenders and he's been good the whole year, but there's been a couple games where he's really elevated his game and this is one of them.
''Not just with the puck, but his physicality ... he was emotionally dialed right in.''
David Perron and Tyler Bertuzzi scored goals for the Red Wings, who have lost two straight after winning seven of eight. Magnus Hellberg had 36 saves.
This matchup of teams chasing a playoff spot in the Eastern Conference was a makeup for the game that was canceled on Dec. 23 due to a snowstorm. The teams meet again here on Tuesday.
Detroit remained three points behind Pittsburgh for the East's second wild card. Buffalo is just a point behind the Penguins, and the Red Wings are in a three-way tie with Florida and Washington with 64 points.
''Everyone's fighting for their lives,'' Detroit's Dylan Larkin said. ''We have teams that we're playing against that are battling for the same spot that we are. It did (feel like a playoff game) on the ice.''
The Red Wings know in order to have a chance Tuesday night they'll need to stay out of the penalty box. Ottawa was 2 for 6 with the man advantage, which helped put the game out of reach.
''Too many penalties,'' Detroit coach Derek Lalonde said. ''That team will lose to nobody in the league if you give them six power plays.''
Perron fired a shot from the left circle on a power play for his 15th goal of the season to give the Red Wings a 2-1 lead at 5:11 of the second.
The Red Wings then scored four goals over an 8 1/2-minute stretch to take control.
''Sometimes when the game is big you don't let it be a big game, you just play hockey,'' Giroux said. ''You don't overthink it and tonight I think we did that. ... We had a game plan and we just followed it.''
Batherson tied it with Ottawa's second power-play goal of the game on a shot from the right circle with 7:25 remaining in the middle period. It was his 19th of the season - 12th on the power play.
Giroux put the Senators ahead for good as he got a long pass from Dylan Gambrell and skated in on Hellberg on a breakaway and slid the puck through the goalie's legs for his 24th with 5:50 left in the period.
Tkachuk took a pass from Giroux and fired it past Hellberg from the left circle for his 25th with 2:19 left in the second to make it 4-2.
''I just wanted to do whatever it takes to help the team win,'' Tkachuk said. ''Whether that was by emotion or physicality or making the play at the right time, but everybody did that tonight.''
Chabot beat Hellberg top shelf for his ninth to give the Senators a three goal lead 47 seconds into the third period and Stutzle got his 27th with 5 minutes left.
Bertuzzi got the Red Wings on the scoreboard first as he skated in all alone on Talbot, cut across the front of the goal and put a backhander in from the left side with 8:12 left in the first period. It was his fourth.
Sanderson tied it on the power play at 3:41 of the second as he got the return pass on a give and go from Giroux and fired a shot from center point through traffic and past Hellberg. It was his fourth.
Red Wings: At Ottawa on Tuesday night to wrap up the two-game series and trip.
Senators: Host Detroit on Tuesday night to finish the two-game series and homestand before playing six of next seven games on the road.
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