Federer, 35, made short work of the British number three in his first match after a six-month knee injury setback.
World number 76 Heather Watson lost her tie against Belinda Bencic 7-5 3-6 6-2 to give Switzerland the victory.
Federer and Bencic then combined to seal the whitewash, beating Evans and Watson 4-0 4-1 in Australia.
The Hopman Cup, played in Perth, comprises two singles matches and a mixed doubles contest between nations in a round-robin format with two groups of four.
France beat Germany in Group A’s other fixture, with USA, Spain, Australia and the Czech Republic completing the line-up in Group B.
It started with an ace, and finished in just 61 minutes, as Roger Federer made a successful and oh-so-welcome return to tennis at the Hopman Cup on Monday night. It was not flawless, but nor was Fed-esque perfection expected or required after six long months away.
Fifteen years after his last appearance in Perth, 35-year-old Federer defeated Britain’s Dan Evans 6-3, 6-4 at the mixed teams invitational in his first match since his semi-final loss to Milos Raonic at Wimbledon. There, the champion Swiss tweaked the left knee that had required surgery in February after a freak bathroom mishap. Here, Federer admitted he was emotional walking out on court, then reluctant to leave, once one of the more anticipated comebacks in recent tennis memory was complete.