The Red Wings (26-37-10), who were eliminated from Stanley Cup Playoff contention last week, have won back-to-back games for the first time since Feb. 12-14. They also defeated the New York Islanders 2-1 on Saturday.
Jimmy Howard made 41 saves to improve to 10-3-3 in 17 career appearances against the Rangers. Frans Nielsen also scored for Detroit.
WATCH: [All Red Wings vs. Rangers highlights]
Forward Taro Hirose, playing in his first NHL game after signing as a free agent out of Michigan State University last week, had an assist on Nielsen's goal for his first NHL point.
"Nobody in the locker room wants to be in this spot a year from now," Red Wings coach Jeff Blashill said. "Well, to do that you've got to get better. There's not instant help coming from the outside generally in this league. It comes from within. What wins do is they give you a little bit of confidence, which helps you play your best, which helps you in turn get better."
Athanasiou has five goals in the past four games, giving him 28 this season. Dylan Larkin has 27 goals. The Red Wings haven't had a 30-goal scorer since 2008-09, when Marian Hossa (40), Johan Franzen (34), Pavel Datsyuk (32) and Henrik Zetterberg (31) all did it.
"His consistency in his engagement has been much better I think than previous years, and I think from Day 1 of camp he was that way," Blashill said of Athanasiou. "When he's engaged he's a really good player. What does engaged mean? Stopping on pucks, winning puck battles, doing those types of things. I think he's done that on a more consistent basis this year than a year ago."