It also gave Switzerland the lead in their Group B tie against the Japanese, before Belinda Bencic sealed the tie for the Swiss with a straight-sets win over Naomi Osaka.
Federer started his 2017 campaign in Perth and given the success which followed, the 36-year-old was keen to replicate his preparation for Melbourne by returning to the Hopman Cup.
Speaking after his 6-4, 6-3 win over the 40th-ranked Sugita, the Swiss star said he was entering the new season more confident in his game than the last.
"I feel much more in a rhythm," he said.
"Last year, I was like I hope I'm going to be able to hit my first serves, and I hope it's going to work out as much as it did in the practice.
"I think all those question marks aren't really there this time around, which is a nice thing.
"I think it was a great start."
While a number of his main rivals, including Novak Djokovic, Rafael Nadal, Stan Wawrinka, Andy Murray and Milos Raonic, have battled fitness issues this year, Federer said his body was in perfect shape heading into 2018.
"I'm healthy and had a great off season," the 19-time Grand Slam champion said.
"The body's great, it couldn't be better, so I couldn't be happier."
Despite his age, Federer added he felt like he was still as competitive as ever.
In the mixed doubles the Swiss completed a clean sweep of the tie with a 2-4, 4-1, 4-3 (5/1) win under the Fast4 format.
Earlier on the opening day of the tournament, the United States pairing of CoCo Vandeweghe and Jack Sock triumphed over Russian duo Anastasia Pavlyuchenkova and Karen Khachanov 2-1 in their Group B tie.
Copyright Agence France-Presse, 2017