Two years ago, the Colombian Falla almost caused one of the biggest upsets in the sport's history when he led Federer by two sets to love in the first round at Wimbledon and served for the match, only for the 17-time grand slam champion to turn it around.
Their rematch looked routine for Federer today when he led 6-3 5-3 and held three match points on Falla's serve, but remarkably he missed them all and was then broken twice in a row to lose the second set.
Falla pegged back Federer again when he went up an early break in the decider but the world number one dug deep and pulled through, taking his fifth match point to win 6-3 5-7 6-3.
The 30-year-old said of the match: 'It was up and down, a rollercoaster match like it was a few years ago. But I never stopped believing, kept on pushing.'
There was a shock in the first match on Centre Court when Belgium's Steve Darcis knocked out sixth seed and former Wimbledon finalist Tomas Berdych.
Czech Berdych had also lost in the first round of Wimbledon to Ernests Gulbis, and he was outplayed again, with Darcis winning 6-4 6-4.
On Court Two, Belgian Olivier Rochus took on John Isner of the USA, and it was the latter who prevailed 7-6 (7/1) 6-4.
Seventh seed Janko Tipsarevic of Serbia and eighth seed Juan Martin Del Potro of Argentina both made it through their opening matches, but Spain's Fernando Verdasco, the 14th seed, was beaten 6-4 7-6 (11/9) by Uzbekistan's Denis Istomin.
Meanwhile, in the women's Singles, Wimbledon champion Serena Williams was cheered on by Michelle Obama as she began her Olympic campaign in style on Centre Court.
The fourth seed had the United States' First Lady in her supporters' box as she defeated Serbian former world number one Jelena Jankovic 6-3 6-1 to make it 12 straight victories.
Williams next meets Poland's Urszula Radwanska, the younger sister of Agnieszka, who the USA athlete beat to win her fifth Wimbledon title three weeks ago.
Two of last year's grand slam champions are already out of the tournament, with fifth seed Sam Stosur and 11th seed Li Na both losing today.
Australian Stosur went down in an epic match against Carla Suarez Navarro, the Spaniard winning 3-6 7-5 10-8, while China's Li was beaten 6-2 3-6 6-3 by Slovakia's Daniela Hantuchova.
In the next round Suarez Navarro will play Kim Clijsters, who is playing in her first and last Olympics before she retires for the second time after the US Open.
The Belgian has struggled with injuries this season but she looked in very good form today against Italy's Roberta Vinci, racing through the first set and then edging a closer second to win 6-1 6-4.
Last year's Wimbledon champion Petra Kvitova, seeded sixth here, was given a fright by Ukraine's Kateryna Bondarenko before coming through 6-4 5-7 6-4.
There were also victories for Caroline Wozniacki, Ana Ivanovic and Vera Zvonareva, the bronze medallist in Beijing, but 12th seed Dominika Cibulkova was beaten by Bulgaria's grass-court specialist Tsvetana Pironkova.
Andy and Jamie Murray crashed out in the first round of the men's Doubles in a very tight battle with Austria's Jurgen Melzer and Alexander Peya.
In the women's Doubles there was also frustration for Great Britain when Heather Watson and Laura Robson lost to Angelique Kerber and Sabine Lisicki of Germany.