Brown scored 12 seconds later to make it 2-1. Ennis gave Ottawa a 3-1 lead at 11:42 off a pass from Brown on a 2-on-1.
"Not a great start. Anderson was great, he held us in the game, but they certainly had a lot of speed," Senators coach D.J. Smith said. "We adjusted and found that speed in the second period. Big power-play goal, which we haven't had a ton from. I thought we played some good defense that allowed us to get some offense."
Oscar Klefbom scored on an Edmonton power play with a point shot through a screen to make it 3-2 at 17:37.
Anthony Duclair scored 1:30 into the third period on a rebound off the end boards to make it 4-2, and Namestnikov made it 5-2 at 11:47.
"It's not the night we wanted, you have to give them credit, they worked extremely hard, they competed and competed harder than us," Oilers defenseman Adam Larsson said. "We need to find a way to win these games. You don't want to go into March and look back at these games. We have to learn from it."