This was a landmark 1,500th career match for the 38-year-old Swiss legend as he chases his 103rd title.
Federer is defending the 2018 title at his hometown event. The victory improved his career record at the tournament to 72-9 and increased his Basel win streak to 21 straight matches.
Federer, who has made the Basel final on all of his last 12 visits, owns ATP titles this season in Dubai, Miami and Halle.
The Monday rout took just 54 minutes with Federer forced to break back in the second set before sprinting to the win.
He will face the winner from Radu Albot and Dusan Lajovic in the second round.
Federer, the winner of the previous two editions, last lost here in the 2013 final to Juan Martin del Potro.