Alex Chiasson and Leon Draisaitl also scored for the Oilers, who improved to 5-0 against the Senators this season. Connor McDavid had two assists.
''We caught (Ottawa) early a couple games when we got the jump on them ... but if you're not willing to work, and you're not willing to work for 60 minutes, they're going to take advantage of that,'' Oilers coach Dave Tippett said. ''So, we have to make sure we got our work boots on and we're ready to go for 60 minutes if we expect to have a chance to win.''
Evgenii Dadonov and Tim Stutzle scored for Ottawa (9-18-1). Thomas Chabot assisted on both goals.
''Our goal was to get out of the first period tied or better. We did that,'' Senators coach D.J. Smith said. ''It's on us. We made a couple mistakes. Can't fault the effort.
''I thought the third period was a good period for us, had a lot of chances. Second period, couple bad changes end up in goals for them.''
The game was the first of three meetings this week between the teams, and part of a tough stretch for the Senators, who play seven games in 11 days.
The Oilers (16-11-0) jumped into second place in the North Division with the victory, a point ahead of Winnipeg.
''We're learning on a nightly basis how to play those games, which is good to see,'' Chiasson said. ''Our group stays in the fight and finds ways to win games when we may not be at our best right off the bat. It's good to see our group maturing.''
After winning 4-3 in Calgary a night earlier, the Senators got off to a strong start. Dadonov got them on the board 56 seconds in when he spun and fired past goalie Mikko Koskinen. It was the second time this season Ottawa scored in the opening minute.
''It's a long game and stuff happens. So you can't get rattled by that,'' Oilers center Kyle Turris said.
Yamamoto tied it with a perfect redirect of a long shot by Darnell Nurse at 7:03 of the first period.
The Oilers took their first lead at 6:03 of the second on a power play when Chiasson beat Joey Daccord on a 2-on-1 for his fifth goal of the season.
Edmonton caught the Senators on a shift change to pad its lead at 14:41 of the second, when Draisaitl fired a quick snap shot inside the right post for his first goal in eight games, and 11th of the season.
Stutzle sent a shot over the shoulder of Koskinen at 17:57 of the second.
''We give up a tough one early, but our guys stuck with it,'' Tippett said. ''We played pretty solid for the most part throughout the whole game.''
Daccord made a few excellent saves in the final minutes to keep the Senators in the game, but they couldn't get the tying goal and fell to 0-6 this season in the second game of back-to-backs.
''He was great. Gave us every opportunity to win,'' Smith said.
Edmonton outshot Ottawa 37-28.
''I like the way we don't get flustered at the end,'' Tippett said. ''We know ... you're going to have to play the whole 60 (minutes) right through it, right until there was a bouncing puck came with about four seconds left.
''That was our mindset after the first period, second period and third period. And you know, the goal is to get two points and we were able to get it. We've got to re-rack and get ready for Game 2.''
The teams play the second game of their three-game series on Wednesday. The finale is Friday.
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