The fourth seed remains on course for another title triumph Stateside, less than a week on from becoming the oldest champion in Indian Wells history.
Federer dug deep against Tiafoe to take the first set 7-6(2), before following that up with a 6-3 triumph in the second for a straight-sets victory.
The opener went the way of the serve throughout, leading to a tie-break that was edged by the 18-time Grand Slam winner to put him on course for a last-32 meeting with either Robin Haase or Juan Martin Del Potro.
Taking on a top-10 ranked opponent for the first time, Tiafoe managed to break Federer in the opening game of the second set, only for the Swiss to hit back with two breaks of his own in the second and sixth games to get safely over the line.
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