Anthony Duclair scored for the Senators (22-38-5), who have lost seven straight. Craig Anderson made 29 saves.
"I think we battled hard, we worked hard, we lost too many one-on-one battles and it showed," Senators forward Mikkel Boedker. "But the effort was there, and they are the number-one team in the League for a reason."
Hedman made it 1-0 with his ninth goal of the season at 7:17 of the first period when he knocked in a rebound off a shot from Dan Girardi. McDonagh increased the lead to 2-0 at 8:51 with a wrist shot off a pass from Cernak.
"The forwards did a good job of getting us involved," Hedman said. "My goal is a perfect example of us moving around and trying to create some confusion and we had a lot of good shifts."
Kucherov had an assist on McDonagh's goal, his 75th of the season. The NHL scoring leader (106 points) is the first player to record 75 assists in a season since Henrik Sedin of the Vancouver Canucks did it in 2010-11.
"It's a good sign that, first and foremost, we're not spending a lot of time in our zone," McDonagh said. "Our forwards have a ton of skill and vision to find us and put us in positions to get pucks to the net. We're fortunate a few of them went in tonight."
Duclair made it 2-1 at 9:28 of the first period when he finished a 2-on-1 with a chip that scored on the far post.
Cernak made it 3-1 with his third goal of the season at 3:15 of the second period. Kucherov followed with his 31st goal of the season to make it 4-1 at 15:27 of the second period.
"We saw [their defensemen] in videos and stuff," Senators defenseman Dylan DeMelo said. "They move around a lot. Top to bottom they have a really good team. That's a team that's going to have a good run in the playoffs."
Sergachev made it 5-1 with his fifth goal of the season at 1:59 of the third period.
Senators forward Bobby Ryan missed a penalty shot at 5:06 of the second period after Kucherov was called for slashing him on a breakaway.
"[Vasilevskiy] made a good save," Ryan said. "I did what I wanted to do with the puck but I missed my mark a little bit. If I score there it kind of changes the complexion of the game a little bit."