The Red Wings extended the lead in the second with a pair of goals from Moritz Seider and Michael Rasmussen before defenseman Rasmus Dahlin buried a one-timer on the power play to put the Sabres on the board with 1:03 left in the period.
From there, the Sabres outshot the Red Wings 15-7 and rallied behind goals from Casey Mittelstadt and Skinner in the third.
Skinner passed across the crease to find Mittelstadt at the back door to make it 4-2. Less than three minutes later, JJ Peterka drew a high-sticking penalty that led to Skinner's goal. Larkin turned the puck over in the Detroit zone, allowing Skinner to go in alone and beat Alex Lyon on the backhand to cut the deficit to one.
"I think you look at that third period, I think we obviously created more opportunities, but we worked for them," Skinner said. "We drew a little more penalties. We had them on their heels. And that's not just one play or just a shift. I think it's shift after shift, us kind of responding and having a little urgency. If we keep doing that over and over, then things will turn around for us."
The Sabres generated numerous chances in the final minutes of play, including a chance that saw Skinner hit the side of the net after attempting to sneak the puck behind Lyon with the extra attacker on the ice and a point-blank opportunity for Dylan Cozens that was blocked in front of the net.
Larkin put the puck in the empty net to seal the Red Wings' victory.
Sabres coach Don Granato thought that the team's mentality changed in the third period and was what made the difference in the opportunities.
"The puck pressure, systematically, way better at pressuring pucks," Granato said about the group's play in the third. "Way more aggressive and assertive handing off the pressure, supporting the next guy to pressure, and more confidence with the puck."