David Pastrnak had a goal and an assist, and Jeremy Swayman made 19 saves for Boston (49-9-5), which leads the Toronto Maple Leafs by 17 points for first place in the Atlantic Division.
"I thought the Oilers were the better team," Bruins coach Jim Montgomery said. "They were good; we weren't good enough. I thought they outplayed us, outworked us and outcoached us. … After the first period, we said, 'We're lucky to be up 2-0.'"
Brad Marchand gave the Bruins a 1-0 lead at 3:51 of the first, slipping the puck between Skinner's legs from the left face-off dot on Boston's first shot of the game.
"Every single game, I've gotten scored on at least once this year," Skinner said. "So, I think having that experience of getting scored on in the NHL -- I mean, the fans go loud, especially here at [TD] Garden -- and just being able to reset like how I always do, and I thought I did a good job doing that."
Boston center David Krejci had a power-play goal overturned at 13:17 after Edmonton challenged for offside.
Pastrnak made it 2-0 with one second left in the period, falling to his back as he shot a one-timer from above the right circle.
"What I recognized is [the Oilers are] really big on [offensive] zone possession," Pastrnak said. "They kind of want to tire you [out] in the [offensive] zone, and just skating around with the puck. It obviously [stinks] for [a] defensive team to be just, you know, running around, but at the same time, you can play it smart, and just kind of stay in the house and wait for them to come to you."