Pavel Datsyuk totaled a goal and one assist as 1, thanks to a three-goal first period.
Jimmy Howard stopped 27-of-28 shots for the win.
Jochen Hecht provided the sole offense for the Sabres, losers in five of their last six.
Jhonas Enroth was tagged for three scores on 35 shots in defeat.
Kindl put the Wings on the board at 8:50 of the opening period when his floater from the left point fooled Enroth and hit the net high to his glove side.
Franzen then netted a power-play score at 13:38 on a wrister from the slot and Filppula struck 63 seconds later for a 3-0 game.
Howard stopped eight shots in the first and nine in a scoreless middle period.
Buffalo finally solved Howard with 6:13 left in regulation, as Hecht took a lead pass from Jason Pominville on the left wing and snapped a shot home.
Datsyuk hit the empty net with 1:17 remaining to lock up the game.
Buffalo travels to Nashville on Saturday and Detroit heads to Colorado on Sunday...The Red Wings last won seven in a row from March 20-April 1, 2010...Detroit has never blanked Sabres in Buffalo, but has gone 8-2-1 in western New York since October of 1996.