The six-time champion at SW19 eventually won 5-7 4-6 6-4 7-6 6-0 after he looked to be heading out of this year’s tournament at the first hurdle, as Falla, ranked 56 places below Federer, served for the match in the fourth set.
Federer, however, broke back and produced a ruthless display after sealing the fourth set on a tie-break, going on the seal the fifth set 6-0.
“I definitely got very lucky today out there,” Federer told BBC Sport. “I’ve lost many matches this year that I should have won. This is one I should have lost, but I came through. That’s sometimes how grass court tennis works.
“I thought I had a few chances early on in the first set, he came up with some good shots and then I struggled really.
“He played really good and was able to neutralise me from the baseline.”
“It’s tough for him, it’s amazing for me because I thought he played incredibly.”
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BIOGRAPHY: Lucas Torreira