Brown's goal streak is the longest in Ottawa history and tied for the 11th longest in the NHL since the 1990-91 season.
"I've never seen anything like it," Senators forward Brady Tkachuk said. "I told him that, at this pace, we're going to have a little bet going. I think he's going to score in the next 13 (games). Nobody deserves it more than him."
Tkachuk scored twice, and Anton Forsberg made 24 saves for the Senators (14-25-4), who ended a four-game losing streak.
"Pretty gutsy win, having been down 2-0," Ottawa coach D.J. Smith said. "A lot of young guys sometimes start going out on their own page, but we didn't tonight. We found a way to get ourselves a win."