Niklas Kronwall's third-period goal broke a tie, and Pavel Datsyuk had a goal and an assist in Detroit's 2-1 victory against the Oilers.
Both Red Wings goals were scored on the power play, and Detroit killed seven of eight short-handed situations. The Red Wings came into Saturday ranked 29th in penalty-killing among the 30 NHL teams.
"I thought we did a pretty good job," Kronwall said. "We would have liked the other one back. Overall we did a good job of staying aggressive and not giving them too much room."
Henrik Zetterberg had two assists, and Jimmy Howard made 23 saves for Detroit (6-4-1).
Rookie defenceman Justin Schultz scored the lone goal for Edmonton (4-4-3), and 40-year-old Nikolai Khabibulin stopped 28 shots in his first game of the season.
"Disappointed, of course, with our specialty teams, which has been very strong this season. Today they deserted us," Oilers coach Ralph Krueger said.
Kronwall's power-play tally at 6:08 of the third period gave Detroit a 2-1 lead. His first goal of the season was scored with a slap shot from the high slot.
The goal came as Edmonton's Chris VandeVelde served a penalty for hooking Justin Abdelkader.
"Mule (Johan Franzen) once again did a great job in front. I finally was able to get one on the net," said Kronwall, who has nine points in 10 games. "We talked a lot about shooting the puck. Mule is going to be there all night long. The rest of us have to do a better job getting pucks in there."
Detroit entered Saturday with the No. 26 power play in the NHL.
The Red Wings killed off a two-man disadvantage that lasted 1:07 early in the third period.
"They had a few chances, but we battled. We tried to keep the shots away, lots of blocks," Datsyuk said. "Our defencemen did lots of blocks, and Jimmy got lots of confidence and made it easy for us with lots of saves.
"We practice penalty kill every practice, so it gets better in the game. We're picking up every day. It's hard to jump right back to the top, but we're taking it step by step."
Schultz and the Oilers know they squandered a prime opportunity for a road win.
"We would have loved to capitalize on that," he said. "We just didn't click on the 5-on-3, We moved it better on the 5-on-4 than the 5-on-3."
His power-play tally made it 1-1 with 2:05 left in the second period. Schultz's fourth goal of the season came on a wrist shot from about 10 feet inside the blue line, while Zetterberg was in the penalty box for holding Corey Potter.
Datsyuk opened the scoring with a power-play goal 8:33 into the second period when he jammed a shot through Khabibulin's pads. Datsyuk's fourth goal came just after Detroit failed on a 5-on-3 power play.
Detroit was 2-for-7 with the extra man.
Khabibulin denied Damien Brunner's tip try with 3:46 remaining in the middle period.
The first period was scoreless. Edmonton's Ben Eager had the best chance when he hit the goal post with about 9:30 remaining.
NOTES: Wayne Gretzky said in a NHL.com interview that Zetterberg is his favourite player of the last 10 years, and that he believes Zetterberg was the best Swedish player in NHL history. ... Detroit forward Todd Bertuzzi didn't play because of back pain. C Darren Helm has been limited to one game this season because of back problems. ... Edmonton C Ryan Nugent-Hopkins returned after missing one game because of an injured shoulder. ... Oilers D Jeff Petry was born in Ann Arbor, Mich., grew up in suburban Detroit, and played at Michigan State. Potter, who is from Lansing, also played at Michigan State. ... Kronwall's goal was his 50th in the NHL. . Datsyuk's two points moved him into sole possession of seventh place on the Red Wings' career scoring list with 730.