"(The Red Wings have) to keep (winning). Tough without big guys but it's important to see we can win without them," Franzen said. "(It's) big for us to see we can win without them."
Cory Schneider made 18 saves for New Jersey, which has lost three in a row.
"We didn't play our best game of the year," Steve Bernier said. "There (are) a lot of bad things around right now, but we need to focus on the good things."
The Red Wings finished with 21 shots while the Devils had only 11.
The 11 shots tied a New Jersey franchise record for fewest shots in a home game.
"We didn't cash in (on) some of our chances. We have to be opportunistic. We have to find a way to score two or three and we didn't do that," New Jersey coach Peter DeBoer said.
"It's easy to look at the shot clock and say that (11 shots on goal is not enough). We've generated 21 shots and generated the same amount of scoring chances. (If the shot clock says) 21, you feel better about it? It doesn't matter."
Franzen snapped a 1-all tie when he scored his ninth of the season with 7:20 left in the third. Standing in the low slot, Franzen poked a Gustav Nyquist pass past Schneider.
"It's always hard to defend when you change sides for the defender so I tried and sneak around the back post and found it through the crease," Franzen said of his goal.
New Jersey led 1-0 at the first intermission on Greene's fourth goal of the season.
Having drawn a high-sticking call on Franzen, Greene weaved his way through all three zones before finishing a give-and-go with Patrik Elias by tipping a centering pass under Gustavsson 13:43 into the game.
"It wasn't our best period but we came out the way we did against a good team (and) we have to take that and build off it. We just couldn't seem (to) build off it and get it going," Greene said.
"They were kind of sitting back on the drop pass, before I gave it to Patty. Tried to make the play to Patty and he made a great saucer over to me, and (I) just tried to hang with it to get it over his pad."
The power-play goal was the only one New Jersey scored on four opportunities with the man advantage.
Detroit drew even at 1-all after Andersson scored with 36 seconds left in the second period. The scoring sequence began when Daniel Alfredsson fired a diagonal cross-ice pass to Drew Miller from the blue line.
Miller attempted two backhands, which Schneider stopped, but the New Jersey goaltender was unable to stop Andersson's jam shot. The goal was the fourth of the season for Andersson.
The game stayed tied until Franzen's goal.
Tatar's power-play score at 18:57 of the third was Detroit's only goal on five attempts with the man advantage. The power play was assessed when Schneider was called for playing the puck outside of the trapezoid. New Jersey disputed the call, and replays showed the goaltender was inside the trapezoid.
"I don't know," DeBoer said when asked whether the NHL should institute an instant replay system on disputed judgment calls. "I'm not looking to solve it, just get it right."
Both Detroit and New Jersey were content to take away the middle of the ice, and as a result, neither team generated much offensively.
"I don't think it was any tighter than any other game," the Devils' Travis Zajac said. "We just didn't execute coming out of our own end sometimes. For us, we have to play in the other end.
"We (needed) to elevate our game as it went on and we didn't."
Detroit improved to 49-56-21-0 against the New Jersey franchise. ... Following the morning skate, DeBoer announced right wing Damien Brunner would be scratched. Brunner, signed to a two-year, $2.5 million deal during training camp, has not scored a goal since Oct. 26, a stretch of 16 games. ... Devils left wing Ryane Clowe participated in the morning skate, marking the first time he skated with the team since being concussed by a Jacob Trouba elbow in the Devils' 3-0 loss to the Winnipeg Jets on Oct. 13. ... Red Wings stars Pavel Datsyuk (concussion) and Henrik Zetterberg (herniated disc) missed their second game in a row with injuries.
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NEWARK, NJ - DECEMBER 06: The New Jersey Devils hold a moment of silence for Nelson Mandela prior to their game...