Emery dropped a weak shot by Nash, and Stepan tapped in the rebound.
Six-and-a-half minutes later, St. Louis tipped in a Dan Girardi shot to increase the lead to 2-0.
"That is a good line, and after they scored the two goals tonight, we did a pretty good job on them," Flyers winger Jake Voracek said. "But it was a little too late. They got two goals, and we have to make sure we do a better job on Friday."
In three games against the Flyers, St. Louis has two goals, or one more than he had in 19 games for the Rangers after being traded from Tampa Bay on March 5. (He had one goal and seven assists in those 19 games.)
"You always want to be on top of your game," St. Louis said, "but it is a tough thing to do it consistently, and you have to work at it."
The adjustment to a new team has taken some time, said Rangers center Brad Richards, his former teammate in Tampa Bay. Richards said St. Louis was out of sorts while he got used to his new team.
That has changed in the postseason.
"Now, he feels he is part of it," Richards said. "It took a while to do it, but now he is talking more and getting to know the guys more."
St. Louis obviously is feeling more comfortable.
"I want to do anything I can to help the team win, making things happen with the puck," St. Louis said. "I am just trying to play a total game."
For the series, St. Louis has two goals and three assists. Stepan has added two goals and one assist, and Nash, who had two assists Tuesday, has yet to score but has four assists.
Much was made before the game of the Rangers' ability to win on the road, and while the players tried to downplay that fact, New York continued a season-long pattern.
The Rangers set a franchise record for road wins, going 25-14-2 away from Madison Square Garden, although two of the road losses were to the Flyers.
The Rangers were 23-8-2 in their last 33 road games, and they continued their stellar play away from home on Tuesday with a major assist from a line that has been unstoppable in this series.