Ottawa allowed one goal facing 5-on-3 power plays against that totaled 4:22, and scored the game-winner with a two-man advantage in the third period.
"Obviously a huge win for our group," Senators coach Paul MacLean told the team website. "The penalty-killing units got a lot of work, the power-play units got a lot of work. ... It was like two or three different games. I think both teams gave the referees an awful lot of work to do, but at the end of the day, we came out with a win."
Clarke MacArthur added some insurance when he scored another power-play goal with 4:02 remaining.
The teams combined to take 16 minor penalties and one double minor, with each totaling 23 penalty minutes and going 2-for-8 on the power play.
"When your special teams can win you hockey games, it's a good sign," Senators captain Jason Spezza said. "It shows that we were organized and focused, and those are all things that are good."
Detroit nearly had another 5-on-3 goal and a 3-3 tie with 8:46 left in the third period, but it was correctly ruled on the ice and confirmed by video that Johan Franzen batted the puck into the net with his hand.
"We had an extended 5-on-3 in the third with a chance and we didn't score," Detroit coach Mike Babcock told Fox Sports Detroit. "The other thing is, you can't kill penalties all night long. ... You deserve what you get, you've got to look out for your stick and you can't be in the box all night, no one gets any rhythm like that."
Detroit ended an eight-game winless streak at home with a 4-3 victory against the Carolina Hurricanes on Thursday but is now 1-2-6 at Joe Louis Arena since Oct. 15.
"It seems like we have played some pretty good games at home, haven't been able to find a way to close a lot of games out," center Darren Helm told Fox Sports Detroit. "That's definitely something we'll have to figure out down the road."
The Senators, who snapped a three-game losing streak, also won 6-1 at Joe Louis Arena on Oct. 23. Ottawa visits the Carolina Hurricanes on Sunday.
"It's still a tough building to play in, but we've had good success here now with winning two in a notoriously really hard building to come into," Spezza said. "So hopefully that gives us some confidence."
The Red Wings tied the game 2-2 on their 5-on-3 goal 1:08 into the third period. Pavel Datsyuk tried to send a pass across the goalmouth; Senators defenseman Jared Cowen went to the ice to block it, but the puck went off his back leg and through goalie Robin Lehner.
Ottawa took a 2-1 lead with goals 1:11 apart in the first period. The first came from MacArthur, who after fanning on his first attempt was able to lift his second over goalie Jimmy Howard at 14:33. MacArthur had carried the puck into the zone and sent it behind the net to Ryan, whose pass to the front came off the skate of Red Wings defenseman Kyle Quincey and back to Ryan, who pushed it to MacArthur.
"It was a great second effort by Bobby," MacArthur said. "He tried to get it to me early; he's got that long reach and was able to get me another one. [Kyle Turris] took the D-man and the goalie kind of out of the net there and I was able to have an empty net, so it was a good play by them."
Three fortunate bounces for Ottawa ended in a goal credited to Chris Neil at 15:44. Senators forward Cory Conacher stole the puck from Helm in the Detroit zone. Conacher passed to Neil, whose shot hit Helm then bounced off each leg of Red Wings defenseman Brendan Smith into the net.
"I thought they had three chances in the first period and two of them went in," Babcock said. "The other team's going to get some chances, that's just the way it is, and you have to find a way to execute and not break down.
"One of them was on a line change where we found a way to mismanage the puck and it ends up in our net; that's a tough one. The other one we have enough people back and once again had a little miscue and it's in our net."
Helm started the scoring at 13:23 of the first. He carried the puck through the neutral zone all the way behind the Ottawa goal, then passed to Tomas Tatar and headed to the front of the net, where he tipped Tatar's wrist shot past Lehner.
Lehner made 34 saves for his fourth win in his past five starts. Howard made 25 stops.
"Robin was very good, obviously," MacLean said. "Robin's responded to challenges that we've given him in the past. We put him in the net in Boston, we put him in the net in Toronto, now we've put him in the net in Joe Louis Arena. Those are stepping stones for him in his career as far as becoming a No. 1-type goaltender."
The Red Wings lost Jakub Kindl to a hip injury in the third period; his status for Sunday's visit to the Buffalo Sabres wasn't immediately known. Forward Stephen Weiss returned to the lineup, and Todd Bertuzzi was scratched with an upper-body injury. Weiss had missed six games with a groin injury. Daniel Alfredsson did not play for Detroit against his former team. He has missed five games with a groin injury.