Foligno took a wrist shot from just above the circle and then put his rebound past diving goalie Brian Boucher with 8:29 left. Boucher had smothered another drive by Foligno a few minutes earlier.
"I just kept going to the net and making opportunities," Foligno said. "I was happy to put that one home."
Winchester sealed the victory with a short-handed, empty-net goal in the final minute. The Senators scored 12 goals in their previous five games, earning their lone win in a shootout against Anaheim.
It was the first shutout this season for the Senators (15-11), who have two wins in their past six games.
"It feels pretty good," Elliott said. "We didn't have a lot of Grade-A scoring chances. We had a lot of shots from outside. To bang one of those in and finally get a bounce and be able to hold them off through power plays and blocking shots. You can't tell how many times guys are blocking shots.
"Those are the types of things that win you games."
The Flyers (14-14) were blanked for the third time in six games. They are 1-3 under new coach Peter Laviolette, who replaced the fired John Stevens a week ago after Philadelphia's two consecutive shutout losses.
"There was a shot, I poked the rebound away and the guy came and I poked it as he was coming in," Boucher said of the winning goal. "It rode up my stick and up, over, bounced and over my glove. It's frustrating for the team right now. We need wins and we're not getting it."
Philadelphia, which lost six of seven before the coaching change, has scored only 11 goals in seven games. Six of those came in a 6-2 victory over the New York Islanders on Tuesday.
"We're playing hard," forward Scott Hartnell said. "We're skating well. Compared to last game, we weren't getting the shots through. We had a couple whacks where their D-men would block us.
"That's just not bearing down enough and getting in front of the net and getting to the hard areas. We have to do a better job, and need to get those greasy goals. It's not going to be tic-tac-toe, and in practice we need to get our nails dirty, get in there."
Philadelphia missed some prime scoring opportunities. One came on a 5-on-3 power play in the first period. Another chance came in the second, when Matt Carle appeared to score in front of a crowded net, but referees ruled that Elliot was pushed into the net by Hartnell.
The play wasn't reviewed.
"Carle shot the puck," Hartnell said. "I saw the goalie when I was in front of the net, the puck was basically between his legs at his goal skates, and before I touched him his goal skates were almost near the back of the net. I just was there pushing [the puck]. From my vantage point, it was in the net."
Hartnell had a chance with 5:47 left in the second period, but Elliott stretched across the net to thwart the backhanded breakaway attempt.
"That wasn't the difference," Hartnell said. "They played pretty hard. They probably blocked 20 or 25 shots. Their D-men were blocking everything, and we just couldn't seem to get those pucks around the net."
The Senators were glad to take the tight victory.
"Any win on the road is a big win, and any win at this time of the year is big," Ottawa coach Cory Clouston said. "We've been struggling a little bit as of late. Brian was real solid. I thought our guys did a real good job of blocking shots and getting in shooting lanes."
X-rays taken on the right wrist of Flyers captain Mike Richards were negative. Richards was checked into the boards by Matt Carkner. ... The last time the Flyers were shut out three times in as few of six games was Dec. 6-14, 1968, when it happened in four games. ... Jeff Carter played in his 243rd consecutive game, the fifth-longest streak in Flyers history. ... Elliott posted his other NHL shutout on March 29 against Tampa Bay. ... Boucher is 1-5-1 in eight career starts against Ottawa.