Darryl Sutter was hired as Ward's replacement.
Dillon Dube scored his first NHL hat trick, and Sean Monahan and Derek Ryan each had a goal and an assist for the Flames (11-11-2), who are 3-5-1 in their past nine games. David Rittich made 29 saves.
"Feels good, but anything at this time with our division right now, I think winning is everything and that that makes it feel even better," Dube said. "If you lost the game and get that, it doesn't mean anything. To get the win with it feels really good."
Josh Norris had a goal and an assist for the Senators (8-17-1), who have lost three of four. Matt Murray allowed four goals on 11 shots and was replaced to begin the second period by Joey Daccord, who made 15 saves.
"I think just overall top to bottom we didn't come ready to play tonight, and it showed in our play," Ottawa defensemen Erik Gudbranson said. "We've got a lot more to give than that. We've got to refocus and come out and have a good game to follow this up, because those are tough ones to be a part of."
The Flames split four straight games against the Senators, the first three played on the road. (Ottawa lost 3-1 at the Montreal Canadiens on Tuesday between the third and fourth games.)
"We just beat them handily in our building (5-1 on Monday), and they come back and they were ready," Senators coach D.J. Smith said. "We weren't ready to stop and start and do all the things that we had to do or that we did the other night. They were the better team today."
Brett Ritchie made it 1-0 2:22 into game when he scored on the rush for his first goal with the Flames. It was his third game since signing as a free agent Jan. 17.
Video: OTT@CGY: Ritchie finishes passing display for goal
Dube scored 37 seconds later from just inside the left face-off circle off a pass from Matthew Tkachuk to make it 2-0 at 2:59.
Norris scored from a scramble in the crease to cut the Flames lead to 2-1 at 5:25.
"Unfortunate start, but we stuck with it and we got a goal there, and all of a sudden it's 2-1," Norris said. "Then you're just playing hockey and not thinking about the score. Then, obviously, the game kind of got a little bit out of hand, and we were just chasing it."
Monahan made it 3-1 at 11:56 when he scored on Calgary's fourth shot of the game.
Video: OTT@CGY: Monahan wires wrister home to double lead
Josh Leivo scored with a shot from the top of the left hash marks that went in off the left post to make it 4-1 with 40 seconds remaining in the first.
"We've just got to play fast with the puck and play in their zone," Tkachuk said. "Anytime you come out of there with a three-goal lead after the first, we'll take that."
Dube extended the lead to 5-1 at 7:16 of the second period when he scored with a backhand from the slot.
He completed the hat trick at 1:17 of the third period when he scored with a short-side shot from the left face-off dot to make it 6-1.
Tkachuk had the primary assist on each of Dube's goals.
"He said he's gonna go look for me, for sure, and I appreciate it," Dube said. "I think we always want to play the right way and to have it work out that way ... but he's such a smart player that he was able to make that cross pass, and I was trying to get open for him, but tons of credit to him and [linemate Elias Lindholm] tonight."
Video: Dubé tallies his first career hat trick vs Senators
Artem Anisimov scored on a power play to make it 6-2 at 2:21, and Ryan Dzingel scored in his first game since being reacquired by the Senators in trade from the Carolina Hurricanes on Feb. 13 to cut it to 6-3 at 6:00.
Ryan scored at 7:05 for the 7-3 final. It was his first game after missing 13 with a broken finger.
NOTES: The coaching change was announced by the Flames after postgame media availabilities had ended. ... Senators forward Drake Batherson had a seven-game point streak end (seven goals, four assists). ... Dzingel scored 126 points (62 goals, 64 assists) in 247 games for Ottawa from 2015-19 before being traded to the Columbus Blue Jackets on Feb. 23, 2019. … Jacob Markstrom, who missed five games with an upper-body injury, backed up Rittich. ... Monahan is one goal from 200 in the NHL. ... Flames forward Sam Bennett was a healthy scratch for the second time this season.
Video: Dube's hat trick sparks Flames' 7-3 rout of Senators