Federer fired five aces and saved three of the five break points he faced to win in 1 hour 28 minutes. It was the 32-year-old's 14th title on grass and 79th overall.
It was also Federer's seventh win from seven meetings with Falla.
The 69th-ranked Falla was the first Colombian to reach the final of a grass-court tournament. He was playing his second on tour after he finished runner-up to
Although Ivanovic started shakily for the second day in succession, and dropped serve immediately, she recovered quickly, her heavy ground strokes and willingness to attack soon dominating her unseeded opponent, who was playing in her first top-tier tournament final.
It was Ivanovic's 37th win and her third title of the year, putting her level with
The Serb couldn't contain her happiness at conquering her doubts about playing on grass. "On grass you really don't have time to hesitate," she said.
"I tried to shorten my swing and move forwards. You really have to go after your shots. It's important to be clear in your mind."