The Flyers raced to a 4-0 lead and chased Buffalo goalie Ryan Miller in the third.
It was a switch from the rest of the series where the Flyers had trouble in the net. They started three goalies in seven games. Boucher won Games 2 and 6 in relief, but was stout for all 60 minutes in the series clincher.
The defending conference champions must wait to learn their next opponent.
Braydon Coburn, Danny Briere, James van Riemsdyk, and Ville Leino all scored against Miller to suck the drama out of Game 7.
The Flyers surely won't complain about a rout.
This was a Flyers team that spent a chunk of the season atop the East standings, not the one that stumbled down the stretch.
Coburn put the Flyers ahead with only 19 seconds left in the first period, and Briere and van Riemsdyk put the game away with goals in the second.
"In the big games, we show up," said Briere, as the crowd roared in approval.
The Sabres never stood a chance in front of 19,966 screaming Flyers fans.
Or against Boucher.
CANADIENS 2, BRUINS 1
In Montreal, Brian Gionta and Michael Cammalleri scored during two separate two-man advantages and Montreal forced a decisive Game 7 in their first-round playoff series with a victory over Boston.
Game 7 is tonight in Boston, with the Bruins looking to beat Montreal for only the ninth time in 33 postseason series.
Dennis Seidenberg scored for Boston, which played more than half the game without ejected winger Milan Lucic but still outshot the Canadiens 32-27.
Boston had taken the lead in the closely contested series with consecutive overtime wins, but couldn't get the equalizer behind a sharp Carey Price despite outshooting Montreal 11-6 in the third period. Price made 31 saves.