After the match, a young fan ran onto the court and attempted to take a selfie with a clearly perturbed Federer before security steered the man off the court.
The boy, as casual as can be, put his hand across Federer's left shoulder as the tennis great was walking off court with his kit bag, and tried to snap several shots of the two of them together with his mobile phone.
Clearly very uncomfortable, the 2009 champion gently rebuffed the boy, stepped back and glanced over questioningly at security guards for help. After a delay of several seconds, one of them grasped the boy around the waist and steered him away.
Facing a player who pushed him to five sets at Wimbledon five years ago, Federer was never threatened, extending his unbeaten run against the 111th-ranked Falla to 8-0 while serving eight aces.
"I love coming here," said Federer, the 2009 French Open champion. "I wasn't broken. I'm happy."
In the third set, Falla called for a medical timeout, getting some deep massage on his right thigh.
Also Sunday, Bosnian Damir Dzumhur advanced when Mikhail Youzhny retired at the start of the third set. Dzumhur was up two sets at that point again the Russian Youzhny, who was a quarterfinalist in 2010.
The Associated Press contributed to this report.