It was Elliott's second shutout of the season and 40th of his NHL career.
"Brian didn't have a lot of saves to make, but he had some tough ones and he made them all," Flyers coach Alain Vigneault said. "I thought the guys in front of him also played a really good game."
WATCH: [All Flyers vs. Red Wings highlights]
Scott Laughton, Kevin Hayes and Matt Niskanen scored for Philadelphia (29-17-7), which is 6-1-1 in its past eight games.
The win moved the Flyers into the first wild card into the Stanley Cup Playoffs from the Eastern Conference, one point ahead of the New York Islanders.
"When we were out in California [at the end of December], I thought we were chasing too many games," Laughton said. "Right now, we're doing what we need to do and finding ways to get two points. We need every point we can, because everyone is going to be fighting down the stretch."
Detroit (12-38-4) was shut out at home for a second straight game and is 0-8-1 in its past nine. Jonathan Bernier made 28 saves.
"I just focus on my own job, but this isn't an easy situation," said Bernier, who has a .939 save percentage in his past 10 games. "Two games with no goals, and today (Red Wings center Valtteri Filppula) has an empty net and hits the guy's skate. I can't think about having to keep out every goal for us to have the chance. I just have to play shot by shot."