Josi made it 2-0 at 17:43, stickhandling past Filip Hronek for his eighth goal of the season.
"It was kind of a broken play," Josi said. "[Fabbro] had the puck and I saw some space, so I jumped into it, and he hit me in a great spot. I had a step on the defenseman, so I went to the net."
Robby Fabbri pulled Detroit within 2-1 at 9:58 of the second period on the power play.
Nedeljkovic kept the Red Wings within one by stopping Philip Tomasino on a breakaway at 19:48.
Nick Cousins made it 3-1 at 2:33 of the third period, beating Nedeljkovic with a backhand from the edge of the crease.
Eeli Tolvanen extended the lead to 4-1 at 7:07, tipping in Fabbro's point shot, but Michael Rasmussen cut it to 4-2 at 8:57.
Fabbro scored his first goal of the season into an empty net at 19:29 for the 5-2 final.
"Every time we got into their zone they beat us down low," Red Wings forward Dylan Larkin said. "They made it hard to get to the net and get off shots, and I think we need to learn from that and take some of that intensity into our game."
NOTES: Red Wings rookie defenseman Moritz Seider left in the third period with an undisclosed injury. Blashill said he didn't expect to have an update until Wednesday. … Hynes said Saros and Ekholm were feeling better after the game and he doesn't expect either illness to be a long-term problem. … Johansen has scored 13 points (two goals, 11 assists) in his past nine games. … Detroit's top line of Fabbri, Larkin and Lucas Raymond finished with four shots. … Red Wings forward Pius Suter had an assist to extend his point streak to six games (one goal, five assists). ... Harpur had one shot in 13:20 and Myers had two hits and blocked four shots in 15:50.