Edmonton went up 4-0 with another power-play goal with seven minutes left in the second frame as Nugent-Hopkins kicked the puck back to Draisaitl in traffic in front and he scored his 23rd.
"By no means is it me beating him", Eichel said, of splitting McDavid and defenceman Oscar Klefbom at the Oilers blue line, before being hooked by Klefbom on his way to the net.
David Pastrnak scored a power-play goal at 3:10 of the first period to give Boston a 1-0 lead.
Oilers coach Dave Tippett didn't question the officials' decision to issue Eichel a penalty shot, by saying Klefbom got in too tight on the Sabres' captain. Linus Ullmark made 32 saves.
The Bruins were also forced to play without Matt Grzelcyk in this one, as the 5-foot-9 defender sat out due to an illness.
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Coach Ralph Krueger didn't have an update on Oloffson status following the game. "I'm trying to defend it. Ref makes a call and that's the way it goes".
Gaetan Haas tied the game 1-1 at 7:41 of the second period. "We capitalized on a couple of chances". The second was even better; the goalie quickly slid across the crease to block his wrister from the right circle at the end of a 2-on-1 break when McDavid had a wide-open shot after a cross-ice pass.
It was almost four years ago in Buffalo when Jack Eichel and Connor McDavid met for the first time in an National Hockey League game, one that turned out to be an overtime thriller the Oilers won because of McDavid.
Jokiharju finished a feed from Reinhart to score Buffalo's first goal 13 minutes into the first period. Leon Draisaitl has collected four goals and five assists over the last 10 games for Edmonton.
Oilers: At the Toronto Maple Leafs on Monday.