Federer fired 10 aces and defeated the fourth-seeded Kei Nishikori 6-3, 7-6 (4) as he improved his record here to 45-5.
"It was played on a very fast court and a few shots were going to decide it. They went my way," Federer said.
Nishikori rallied to force the second set to the tiebreak, where he made a mini-break at 4-2, only to let Federer off the hook with two consecutive forehand errors.
Federer miscalculated the score and hadn't realized he won.
"The crowd's applause was different, I looked at the referee and he was smiling, then I noticed Nishikori was at the net. I had to check the score. Of course, I was happy to accept the win," said the Swiss, who thought it happened for "probably the first time."
After a first-round bye, Federer began his Wimbledon preparations by defeating Portugal's Joao Sousa on Thursday then had a walkover in the quarterfinals.
Falla rallied to beat 2011 champion Philipp Kohlschreiber 5-7, 7-6 (5), 6-4 to become the first Colombian to reach the final of a grass-court tournament.
"It's an amazing feeling," Falla said. "I knew I had good chances here. I already played great matches on grass courts. It's my favorite surface."
The 69th-ranked Falla saved six of the nine break points he faced before defeating Kohlschreiber in 2 hours, 21 minutes.
"He took the big points and that makes the difference," Kohlschreiber said.
Sunday's final against seven-time Wimbledon winner Federer will be Falla's second on tour after he finished runner-up to Ivo Karlovic at Bogota in 2013.
"It would be nice to play Roger, maybe to get revenge for the last couple of matches on grass at the Olympics and at Wimbledon," Falla said, referring to their previous meetings in 2012 and 2010.
Federer has a 100 percent record from six meetings with Falla.
Federer, who made his debut at the tournament 14 years ago, will be playing for his 79th title and his seventh from 12 appearances in Halle.
With Switzerland playing Ecuador in the World Cup at 6 p.m. German time and the final getting underway at 3 p.m., Federer said he'd have to play quickly -- he's also playing in the doubles final -- so he can watch the football.
"Whoever wins the first set is the winner," he joked.