Eichel slid a rebound by Daccord's left leg to extend it to 4-2 at 11:06 of the third period, and Jason Pominville pushed it to 5-2 from the right wall at 12:57.
"I've really enjoyed every moment," said Pominville, who received a standing ovation after his goal and its announcement. "I don't know what the future holds, but enjoy the next couple of days and hopefully get another win."
Pominville was possibly playing his final home game for the Sabres. The 36-year-old can become a free agent this offseason.
"I'm so happy for him, not because he scored, but just the way that line played tonight," Buffalo coach Phil Housley said. "They were tenacious, got a couple good looks. I know the goal he scored wasn't one of those highlight reels. But just a great guy, great human. It was great to see him contribute tonight."
Anthony Duclair tipped in Cody Ceci's shot from the blue line to give the Senators a 1-0 lead at 2:03 of the first period.