Bryzgalov made 30 saves to notch the win as the Flyers lifted their points streak to eight games (6-0-2).
Jagr, who had 13 points (six goals, seven assists) in his previous 10 games, played three shifts and did not return. The Flyers said he had a lower-body injury - it is believed to be a groin strain - and would not give specifics.
The Flyers took a 1-0 lead when James van Riemsdyk, after taking a feed from Claude Giroux, scored from deep inside the right circle with 7 minutes, 23 seconds left in the second period. Skating down the right side on a two-on-one, van Riemsdyk used Kimmo Timonen as a decoy and beat Smith (40 saves) with a high shot to the short side.
Bryzgalov and Smith were brilliant in the first two periods, combining top stop 50 of 51 shots. Bryzgalov stopped all 22.
Phoenix tied the score 3:38 into the third period as Mikkel Boedker scored from a bad angle out front, knocking a loose puck through Bryzgalov's legs after the goalie appeared to have it covered.
Earlier in the day, Coyotes defenseman Derek Morris said, "We have to throw a lot of pucks at Bryz. He's known for letting in bad goals, you know," according to Broad Street Hockey.
Bryzgalov, 31, played most of his previous four seasons in Phoenix.
Morris was also quoted as saying he was "glad he's gone because the guy we brought in has done a great job and fitted in really well, made our team even closer. There was some animosity there with Bryz sometimes. We don't have that with [Smith]. So we have a good group, and we're winning games because of it."
Going cheaper doesn't necessarily mean you are going to get less quality. At least that's how it has worked with the Coyotes and their goaltending situation.
The Coyotes couldn't afford to pay Bryzgalov, so they traded him to the Flyers and later signed the 29-year-old Smith, who has been primarily a backup in his career.
Smith has not played like a journeyman this season. The 6-foot-4, 218-pound goalie entered Thursday with an 8-2-3 record, a 2.19 goals-against average and a .933 save percentage.
Smith signed a two-year deal for a total of $4 million. Bryzgalov signed a nine-year pact for $51 million.
Jagr's injury caused the Flyers to scramble their lines. Sean Couturier and van Riemsdyk were among the players who replaced Jagr on a line with Giroux and Scott Hartnell.
The Flyers killed all four Phoenix power plays in regulation, making them 34 for their last 35 in the last eight games.
Contact staff writer Sam Carchidi at email@example.com or on Twitter @BroadStBull.