"To be able to play Federer again is simply top," said Haas, the oldest player in the singles draw at 34.
Federer is aiming to win his 75th tour title, only two behind all-time leader John McEnroe.
"That would be nice but I want more titles. If I only get three more, then the years ahead don't look too good for me," Federer said, joking.
After winning the first set on a tiebreaker, Haas got the decisive break in the 11th game of the second set to lead 6-5 before wrapping up the match.
"I said it all week that Tommy's playing fantastic tennis," said Kohlschreiber, who knocked out Rafael Nadal on Friday.
Earlier, the second-seeded Federer broke Youzhny twice to wrap up the first set in just 21 minutes. The Swiss was in such control that one fan implored him to slow down.
The 16-time Gram Slam champion responded by breaking twice more, before dropping serve to lead 5-3.
Federer wasted three break points in the next game, but sealed the match in the following one with his eighth ace.
"It was nice to come out and play some decent tennis after yesterday's shootout drill," Federer said, referring to his tiebreaker win over Milos Raonic of Canada in the quarterfinals.
The 29-year-old Youzhny has never beaten Federer in 13 attempts.
"Mikhail played a great tournament, and he deserves respect for the way he fought back in the second set," Federer said.
Federer's only final defeat at Halle was to Lleyton Hewitt in 2010. He is bidding for his fifth title of the season after wins in Rotterdam, Dubai, Indian Wells and Madrid.