The Swiss world number two, the top draw at the new claycourt event, needed two hours 28 minutes to set up a semi-final against eighth seed Diego Schwartzman.
Argentine Schwartzman won only seven points in a dreadful opening set against Colombia's fourth seed Santiago Giraldo but triumphed 0-6 6-2 6-2.
Second seeded Bulgarian Grigor Dmitrov eased into the semis with a straightforward defeat of Croatian Ivan Dodig and will face Pablo Cuevas on Saturday.
Organisers will no doubt be hoping for a Federer/Dimitrov showdown on Sunday as the tournament tries to establish itself on the ATP Tour.
Federer, who was photographed on the ATP website visiting some of the city's many attractions, is clearly a fan, even if he was not completely happy with his form.
"They were perfect playing conditions today," the 17-times grand slam champion said. "Almost no wind, beautiful sunshine; not to hot, not too cold.
"Just because it's nice weather doesn't mean you're going to play nice. I wish it was like that, but it's not as simple as that. It was a good fight today."
(Reporting by Martyn Herman, editing by Pritha Sarkar)
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