Tuch scored from the right wall to cut it to 3-1 at 11:27.
Verhaeghe scored into an empty net with 1:38 remaining for the 4-1 final.
"The whole game, we didn't have the emotional energy that we had," Buffalo coach Don Granato said. "It's two weeks in a row now, really big highs on a Saturday night (5-3 win against the Nashville Predators), two days later on a Monday, we couldn't get the energy, the emotional energy. … If you're not on, you don't feel yourself, don't complicate the simple. Start putting pucks to the net and go in there. Put pucks deep, make sure you're working hard without the puck, and we were challenged to do that tonight. When we've struggled, that's been the challenge."
NOTES:Tkachuk has 44 multipoint games in the regular season since the start of the 2021-22 season, fifth-most in the NHL in that span behind Connor McDavid (68), Leon Draisaitl (50), Auston Matthews (49) and Kirill Kaprizov (46). … The Panthers have won six straight games against the Sabres dating to Dec. 2, 2021, their third-longest active streak against an opponent (eight straight wins against the Detroit Red Wings; seven straight against the San Jose Sharks). … Buffalo has lost four straight games at home. ... Tuch set an NHL career high with his 21st goal of the season, eclipsing his previous high of 20, set in 2018-19 with the Vegas Golden Knights.