Larkin and Andreas Athanasiou scored in the shootout for Detroit after Buffalo forward Evan Rodrigues tied it 3-3 with 47 seconds left in the third period.
"It feels good," Larkin said. "We had a good start, good first two periods, and then I think we just let our foot off the gas there a little bit in the third. … Wish we made it a little bit easier for us tonight and little easier on goalie Jonathan Bernier] there, but we stuck it out, played good defensively in overtime, and won it in a shootout. Two points is two points right now for us."
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Tyler Bertuzzi scored, and Bernier made 29 saves for the Red Wings (13-38-4), who were 0-8-1 in their previous nine games.
Jonas Johansson made 18 saves in his first NHL start for the Sabres (23-23-8), who have lost two straight and are 1-4-1 in their past six games.
"We definitely cannot be pleased with losing in [a shootout] here today," Buffalo coach Ralph Krueger said. "The storyline was against the opportunities that we had; we had a lot of opportunities in the first two periods where we were unable to finish. … It's the failed opportunities, the grit we need to finish on those opportunities, that is definitely the reason for this loss today.
"It was a good reaction in the third coming back from two down, it was a good reaction to score 6-on-5 to bring it into overtime under the circumstances, but we shouldn't have been in those circumstances."
Larkin gave Detroit a 1-0 lead at 4:23 of the first period when his shot from along the left boards went through the legs of Luke Glendening, who was screening Johansson.