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The Oilers host the Colorado Avalanche on Thursday. The game can be seen on Sportsnet One and heard on 630 CHED and the Oilers Radio Network.
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Ryan Strome and Jujhar Khaira each scored their ninth goals of the season, while Cam Talbot made 42 saves.
Edmonton went 3-for-3 on the penalty kill and 0-for-1 on the man advantage.
The club lost the faceoff battle, winning 34 percent of the draws.
Kris Russell played 19:57, had five blocked shots, three hits, two shots on goal and one post in what was his 700th career NHL game.
Entering the matchup, the Oilers had been undefeated when leading after two periods. The club is 13-1-0 now due to Boston's third-period onslaught, as the visiting side erased a two-goal deficit and added a winner late.
"Once we got the 2-0 lead and came in from the break, I didn't think we were very aggressive," said Oilers Head Coach Todd McLellan. "I thought we were playing more to protect. We weren't assertive enough, we didn't play in their end enough and we didn't pressure them below the goal line."
Despite only having two shots on goal with less than two minutes to play in the opening frame, the Oilers opened the scoring for the first time since Feb. 5.
Brandon Davidson was in the box for embellishment, while Torey Krug served a minor for slashing, causing 4-on-4 hockey.
Strome took advantage of the open ice, skating in on his off-wing and releasing a wrister low glove on goaltender Anton Khudobin. The unassisted marker made it two straight games Strome had scored - the first time he's done that all season.
Edmonton ended the period with three shots on goal, leading 1-0.
"When we dictate pace, we're a good team," said Russell. "We showed that in the first - we had a lot of shots blocked - but we were playing and getting pucks deep."