Forward Joe Thornton had a goal and an assist in his return to the Toronto lineup after missing 10 games with an upper-body injury.
"A new day tomorrow," Thornton said. "I'm sure we'll look at some film tomorrow, work on some stuff and be ready for Wednesday."
The Senators and Maple Leafs are scheduled to play the second of a three-game set here Wednesday.
Matthews scored on the power play with 59 seconds left in the second period to make it 5-1, but Paul cut it to 5-2 when he scored shorthanded with nine seconds left in the period.
Artem Zub made it 5-3 41 seconds into the third period when he came out of the penalty box and scored on a breakaway for his first NHL goal.
"Getting that goal, all of a sudden you're thinking, 'Oh boy, maybe there's a chance,'" Ottawa coach D.J. Smith said. "And then we capitalized on our chances. There's been a lot of games we've played well or better than the other team and should win. Tonight's not one of those nights, but it was due to come our way."
Brown got the Senators within 5-4 at 5:52 when he one-timed a pass from Colin White.
"When we got the fourth one, you could see the bench going, 'Wow, we're in this,'" Smith said. "It's hard to believe when you're down the way we were. And then all of a sudden, we got our legs, and that's what momentum does."
Keefe said he could sense bad habits seeping into Toronto's play even before Ottawa gained momentum.
"It's as bad as I'd felt about a 5-2 lead as probably I ever had," Keefe said. "We had a talk as a team about cleaning things up for the third period. I thought we were in the right frame of mind, but giving up a shorthanded goal makes it tougher than it needs to be."