Federer, one of 39 players in their 30s in the men's draw, breezed through the first two sets and though Falla had a break point in the fifth game of the third, Federer snuffed out the danger to roll through to round two.
While the "selfie seeking" fan soured his day, Federer was happy enough with his form.
"Winning a match like this is a good thing," Federer, ever-present at majors this century, said.
"I hit a lot of balls today. Clearly hope that I will start to play better and better as the match, as the tournament goes on."
conveniently in the opposite side of the draw to nine-times champions
Rafa Nadal, world number one Novak Djokovic and third seed Andy Murray,
will have a few days off before a clash with Spain's Marcel Granollers.
eighth-seeded compatriot Stanislas Wawrinka, one of several players to
beat Nadal on clay this season, was a 6-3, 6-2, 6-3 winner against
Turkey's Marsel Ilhan.
Japan's Kei Nishikori, the biggest threat
to Federer in the bottom half of the draw, beat French wildcard
Paul-Henri Mathieu 6-3, 7-5, 6-1 before local favourite Jo-Wilfried
Tsonga rounded off proceedings against Swedish qualifier Christian
Lindell with a 6-1, 6-2, 6-2 win.
Germany's Philip Kohlschreiber,
beaten by Murray in a marathon match here last year, dropped only three
games against Japan's Go Soeda, while Spain's Roberto Bautista-Agut beat
German Florian Mayer, also in straight sets.
Mikhail Youzhny's tournament did not last long. He quit when trailing
Bosnia's Damir Dzumhur 6-2, 6-1, - smashing his racket into his forehead
several times as his frustration boiled over.
Former champion Ana
Ivanovic of Serbia, seeded seventh, reached the second round by beating
Kazakhstan's Yaroslava Shvedova 4-6, 6-2, 6-0.