"I knew something was going to go in eventually," said Rodriguez, who had gone 33 games without a goal dating to last season. "You just keep reminding yourself and keep believing you can do it.
"Obviously, it was nice to get a couple to go in and hopefully it continues."
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Rodrigues had a chance to finish off his first career hat trick with 5:12 remaining in regulation, but Jimmy Howard made the save.
"I knew I had space, so I tried to turn and it get it on net quickly enough to fool him," Rodrigues said. "I was going for it, but it wasn't meant to be."
Curtis Lazar had two assists, and Linus Ullmark made 21 saves for the Sabres (20-19-7), who had lost two straight and six of their previous eight.
"The way we played last night got us going," said Buffalo coach Ralph Krueger, whose team allowed four third-period goals in a 6-3 loss to the Vancouver Canucks on Saturday. "It was very disappointing and we had a pretty serious morning.
"I think everyone understood the messages going around."
Howard made 22 saves for the Red Wings (12-31-3), who had won three in a row at home.
Howard, who is 0-10-1 with a 4.79 goals-against average and .856 save percentage in his past 11 games, was a late starter after Jonathan Bernier aggravated a lower-body injury sustained in a 3-2 shootout win against the Ottawa Senators on Friday.
"[Bernier] seemed OK yesterday but woke up and it was much worse, so Jimmy was thrust into action," Red Wings coach Jeff Blashill said. "He's been working hard in practice, but it is tough when you aren't expecting to play."
Rodrigues gave Buffalo a 1-0 lead at 2:39 of the first with a one-timer off a pass from Lazar, who collected the loose puck after knocking over Red Wings defenseman Filip Hronek.