One of these teams will end its slide Sunday night when they meet in Philadelphia.
Philadelphia (11-14-1) never recovered from a bad start in Saturday's 3-0 loss at Boston. The game was scoreless midway through the first period before the Flyers yielded all three goals in a span of 2 minutes, 18 seconds.
"You look down the bench and everyone's heads were down and it just seemed like we were real deflated right from that bad, and that's not what good teams do," winger Scott Hartnell said. "It's on us to pick each other up and to support each other and just be positive and it just seemed like it was down 1-0 and it seemed like we just packed it in."
Philadelphia held a team meeting after the loss as it tries to avoid its first four-game slide in two seasons.
"It's always good when you have a meeting," captain Claude Giroux told the league's official website. "You want to make sure everybody's on the same page, and that's what we did."
While the Flyers' defeats in their streak have all come in regulation, Buffalo (9-13-3) is 0-1-2 in its last three. The Sabres have played six straight one-goal contests, and are 3-3-2 under interim coach Ron Rolston.
"You throw the first two games out, Toronto and the Islanders, in the last six, we've gotten eight points," Rolston said. "And when you look at those games, potentially we should have had 10 points of 12."
One area that remains a concern for Buffalo is a power play converting a league-worst 12.2 percent of its chances, and an Eastern Conference-low 8.7 percent on the road. That unit has scored in consecutive games for the first time under Rolston, whose team has not played since Thursday's 3-2 shootout loss at New Jersey.
"Certainly we're seeing some better things there, better puck movement, more options for the power play now and I think that's going to continue to grow," Rolston said.
Buffalo's best effort with the man advantage came in its season opener, a 5-2 victory over Philadelphia on Jan. 20. The Sabres went 3 for 6 in that game, and Tyler Myers' power-play goal broke a tie with 5:03 left.
Thomas Vanek set a career high with five points in that contest as Buffalo snapped a four-game losing streak to Philadelphia. Vanek, who has 13 points in his last seven games against the Flyers, ended a season-worst six-game drought without a goal Thursday.
Philadelphia's Jakub Voracek was held without a point Saturday for just the second time in his last 11 games. He has 19 points in that span.
Flyers coach Peter Laviolette was critical of his club's effort after it was shut out for the second time this season. Philadelphia has allowed seven straight goals since leading Pittsburgh 4-1 after one period Thursday.
"We were looking for a response from last game and that was not the response we were looking for," Laviolette said.