Federer, who won in a stroll over Rafael Nadal just over a week ago in the Shanghai final, continued his top form in front of the local crowd at an event he has won seven times.
The 36-year-old Swiss, who has competed in a dozen Basel finals, made quick work of his 19-year-old opponent, who had taken him to five sets in this year's US Open first round.
Federer will next face France's Benoit Paire, a 6-3, 7-6 (7/4) winner over American Steve Johnson.
"As long as I'm winning, it's all good. I'm just happy to win the first match. Frances was tough in the US Open.
"The next round with Paire will be tough, he's a dangerous player indoors. I'm happy I've found my rhythm early in Basel."
Defending champion and second seed Marin Cilic advanced in just 30 minutes after German Florian Mayer quit when trailing 6-3.
Third seed David Goffin defeated German Peter Gojowczyk 6-2, 7-5 and fifth seed Jack Sock of the US rallied past Canadian Vasek Pospisil 3-6, 7-6 (9/7), 7-5.
Against Tiafoe, whom he also defeated last March in Miami, Federer wasted no time in establishing domination of the young gun.
The Swiss quickly rolled 4-0 ahead, with Tiafoe finally earning a game after 21 minutes of play.
Federer then produced a love game and closed out the set in 29 minutes on his first set point.
Tiafoe's resistance stiffened slightly in the second set, with Federer achieving the break in the eighth game for 5-3 before wrapping up victory in 61 minutes.
- Del Potro eyes more success -
Juan Martin del Potro, the winner in 2012 and 2013, said he is hoping to build on his recent momentum as the injury- plagued Argentine bids to snatch a place for next month's ATP Finals in London.
The former US Open champion said that the left wrist on which he fell hard a fortnight ago in a Shanghai semi-final loss to Federer is not giving him problems.
The 29-year-old is seeded fourth at the St Jakobshalle and showed that his fitness problems are behind him by beating Grigor Dimitrov to win his second straight Stockholm Open title at the weekend.
"I just want to keep winning events," Del Potro said.
"I'm not thinking of London, it was not one of my goals this year. I know I'm getting closer, I'm just fighting to win all my matches.
"My goal is to play a good tournament here. I will see how far I can move (in the points race to London).
"I must also see how I feel for Paris (next week's final Masters tournament of the season). I will be playing for four straight weeks, that's something I've not done for three or four years."
Out of the possible qualifiers he stands 11th, as Andy Murray, Novak Djokovic and Stan Wawrinka have all ended their seasons due to injuries.
Del Potro is 470 points behind Pablo Carreno Busta, who currently holds the eighth and final spot for London, with 500 points available to the Basel champion.
Disclaimer: No Business Standard Journalist was involved in creation of this content
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