Matthew Tkachuk scored, and Jacob Markstrom made 30 saves for the Flames (17-11-6), who have lost four in a row.
"It's definitely not the way we want it to be right now," Tkachuk said. "Thank God we had the start [to the season] we did, it will keep us kind of in it still. There's no panic by any stretch, but we want to fix this and only have eight [games] left before All-Star [Weekend], so we'd love to get this figured out soon so we can go on a little bit of a roll before that All-Star break."
Paul scored 1:43 into the first period on the first shot of the game to put Ottawa up 1-0. He shot under Markstrom's right arm from the slot after Brett Ritchie turned over the puck inside Calgary's zone.
He made it 2-0 at 16:37. Flames forward Mikael Backlund turned over the puck inside Calgary's blue line, leading to Brown setting up Paul to score around Markstrom on a backhand.
"We try to hunt the puck, get it back, and try to create through that. We did a good job of that," Brown said. "We did a good job of getting pucks back and making it tough on their [defensemen] to break out and turned it into some offensive chances, and we were able to capitalize."
Paul's goal came after Murray made a blocker save on Noah Hanifin in the high slot at 4:01, a glove save on Johnny Gaudreau at 6:00, and a left-pad save on Ritchie at 6:40.
In the second period, Murray made a save on Oliver Kylington at 9:39, after Gaudreau fed Kylington with a backdoor pass.
"He was awesome," Paul said of Murray. "They had some pushes at times where he came up big, sliding across, making some great saves, keeping us in it. When he does that, it gives us energy. We want to play for him, and then it turns into us going into the offensive zone, us making plays, and one, two, three chances at the net. He was a big part of our win tonight. He made some really big saves and held us in it."
