Mika Zibanejad and Kyle Turris also had shootout goals for the Senators. Clarke MacArthur scored in the third period, and Andrew Hammond, who missed the previous two games because of a lower-body injury, returned and made 16 saves.
Petr Mrazek stopped 33 shots for Detroit, which got a regulation and shootout goal from Gustav Nyquist. Tomas Tatar also scored in the shootout.
Nyquist opened the scoring early in the second when his wrist shot zipped past Hammond's right side. Ottawa's MacArthur tied it late in the third when his slap shot nicked Mrazek's glove before going in.
The win, coupled with Boston's 3-2 victory over Florida, kept the Senators three points behind the Bruins in the race for eighth place in the Eastern Conference.
The Red Wings' lead on Boston for third place in the Atlantic Division is two points.
Detroit defenceman Drew Miller left the game early in the first period after being cut by Stone's skate. The Red Wings said he sustained two deep lacerations near his right eye, but his vision wasn't affected.
The Red Wings also were missing centre Pavel Datsyuk, who was scratched because of a lower-body injury. He played in the previous two games after returning from a five-game absence.
NOTES: Red Wings great Gordie Howe celebrated his 87th birthday. A message of thanks from the Hockey Hall of Famer was shown on the arena video board. ... Ottawa forwards Milan Michalek (upper body), Chris Neil (broken thumb) and Matt Puempel (ankle) didn't play. . Detroit's Riley Sheahan returned after missing two games due to an upper-body injury. Fellow forwards Erik Cole and Riley Sheahan were scratched because of upper-body injuries.