Top-seeded Federer cruised to a 6-1, 6-3 win over 40th-ranked Benoit Paire in 57 minutes.
Federer took his second match-point chance on Paire’s serve, approaching the net to hit a forehand crosscourt winner.
Federer has not faced a break point this week in two matches at his hometown event in Basel. He next plays another Frenchman, seventh-seeded Adrian Mannarino.
Mannarino advanced to Friday’s quarterfinals after beating Canadian teenager Denis Shapovalov 4-6, 6-1, 6-2.
Fourth-seeded Del Potro, a two-time Basel champion, beat Julien Benneteau 6-4, 6-4 and stayed on course to qualify for the ATP World Tour Finals lineup in London next month.
Also Thursday, Marin Cilic, the second-seeded defending champion, beat 54th-ranked Borna Coric 6-3, 3-6, 6-3 to improve to 5-0 against his Croatian compatriot.
Cilic will play Hungarian qualifier Marton Fucsovics in the quarterfinals. Fucsovics advanced when opponent Leonardo Mayer retired when trailing 3-0 in the first set.