Earlier in this road trip, the Flyers scored 4-3 shootout wins over Edmonton and Vancouver.
Scott Hartnell said coach Craig Berube had a team meeting before the road trip, telling the players they needed to play with more of an edge on the road.
"They're finding ways to win and they're a confident team right now," Berube said.
Since their franchise-worst 1-7 start, Team Turnaround is 19-9-4 and has moved to within one point of second-place Washington in the Metropolitan Division.
Hartnell tipped in Luke Schenn's point drive to increase the lead to 3-1 midway through the final period, helping the Flyers improve to 5-0 in Calgary since 2001. Braydon Coburn added an empty-net goal.
Calgary ended a scoreless streak of 159 minutes, 35 seconds in the second period, but it has managed just one goal - total - in its last three games.
Brayden Schenn had a first-period goal taken away by a controversial referee's call, but he gave the Flyers a 2-1 lead by scoring on a turnaround shot from the high slot with 1:29 left in the second period.
Meszaros nearly fanned on his shot, but the puck went to the opportunistic Schenn.
"I spun and shot, and I guess good things happen when you put the puck on the net," he said.
Schenn has goals in two straight contests - after failing to score in his previous 16 games.
"It happens to most guys - you go though slumps and then you get a shot of confidence," said Schenn, who had 15 relatives and friends at the game.
Calgary controlled most of the second period and had tied the score at 1-1 when rookie center Sean Monahan converted a Vinny Lecavalier turnover into a goal, scoring from the left circle as he skated on a two-on-one rush with 5:30 remaining in the second.
Just like he did Monday in Vancouver, Mark Streit opened the scoring, blasting a drive that went over the glove of Reto "Yogi" Berra just 3:15 after the opening faceoff. It was Streit's fourth goal in the last eight games, and his fifth of the season.
It was the 10th goal scored by a Flyers defenseman in the last 12 games.
A wide-open Streit faked a shot before scoring after Schenn made a nice play near the wall and fed him the puck.
With about 4:30 left in the first period, the Flyers thought they had taken a 2-0 lead as Schenn, following Hartnell's shot, knocked a rebound into an empty net. But the goal was wiped out when the officials ruled that Hartnell had bumped into Berra.
Hartnell barely touched the goalie and he complained loudly.
Emery, making just his second start since Dec. 12, had to make only seven first-period saves, but he looked sharp. He made his best first-period stop on Mike Cammalleri's shot, and midway through the second period he made a sliding save to deny Jiri Hudler on his shot in front.
Flyers winger Matt Read was injured late in the first period when he apparently took an elbow to the head. Read did not return to the game, and the Flyers would say only that he had an upper-body injury.