Larkin has nine points (six goals, three assists) during a five-game point streak.
Robby Fabbri also had a goal and an assist, David Perron had two assists, and Ville Husso made 41 saves for the Red Wings (25-20-8), who have won four straight since losing 5-2 to the Oilers on Feb. 7.
"Just winning on the road is difficult, let alone against a team like that with the type of offense they have," Detroit coach Derek Lalonde said. "There are moments when they put you on your heels, and it's important for the next shift or the next guy to step up, and I thought for the most part we managed the game fairly well tonight, and Husso was probably the difference in a tight game on the road."
Ryan Nugent-Hopkins had two goals and an assist, and Jack Campbell made 19 saves for the Oilers (30-19-6), who have lost two straight and three of four (1-1-2). Connor McDavid had two assists and has 99 points (42 goals, 57 assists) in 55 games this season.
"We had control of a lot of parts of that game. We generated enough chances to win, but we were a little sloppy on some of our details," Edmonton coach Jay Woodcroft said. "They have to get corrected, there is no excuse for them. We can be better in those situations, and the individuals responsible understand that. We lost the special teams game, which isn't conducive to winning hockey games."