His straight-sets victory over Japan's Yuichi Sugita showed Federer was sharp for his upcoming Australian Open title defence, capping off an extraordinary year in which he claimed two Grand Slam titles and climbed back to number two in world rankings.
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.
"I feel like the game has evolved again and I've made some adjustments," he said.
"I am trying to hit through the backhand more and have a bit more pop on the serve."
Federer only needed one break in each set to slip past Sugita in just 66 minutes and while he looked a fraction rusty at times, he also produced a number of classy strokes to delight a sell-out crowd and show he would again be a force next year.
Bencic, ranked 98th in the world but continuing to rebuild her career after wrist surgery this year, then edged her way past Osaka, ranked 30 places higher at 68, winning 7-5, 6-3 in 91 minutes.
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.
The American pair were beaten in the previous Hopman Cup final at the start of the year and world number 10 Vandeweghe kick-started their bid to go one better with a 6-3, 6-3 win over Pavluchenkova.
Sock, ranked eighth in the world, then overcame a second-set lapse to beat Khachanov in three sets, 6-4, 1-6, 6-3.
The Russians had a consolation victory in the mixed doubles rubber.
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