Federer looked primed for his Australian Open title defence when he came from a set down to beat world number four Alexander Zverev in the men's singles, before Angelique Kerber accounted for Belinda Bencic in straight sets to level the tie against Germany.
The Swiss duo then claimed the tournament with a straight-sets win in the deciding mixed doubles.
For the 36-year-old Federer, it was a second title in Perth, having also been part of Switzerland's previous victory back in 2001, when he teamed with Hingis.
At that time, Federer was just 19 and was yet to win at an ATP event. He said the time spent with Hingis in Perth had a profound effect on his career, which now includes 19 Grand Slam singles titles.
Hingis was the youngest ever Grand Slam champion and world number one, spending 209 weeks at the top of women's tennis and winning five Grand Slam singles titles.
Federer visited Perth with Hingis twice, once as a hitting partner and then in 2001 as her team-mate, and said it shaped his career.
"I could look up to her and think, wow, how is she being so mentally strong and so consistent at such a young age," the Swiss star recalled.
"It made me also believe with hard work and dedication you get really far, because I didn't believe it that much at that point when I was younger, I thought it was more all talent," he added.
"Definitely she helped me to become the player I am today."
Federer was thrilled to add a second Hopman Cup to his glittering resume and said it was a very different feeling to the first.
"It is totally different to when I won it with Martina because I was the apprentice and she was the master," he said.
Unbeaten in his three singles matches in the tournament prior to the final, Federer dropped the first set against the 20-year-old Zverev, but recovered to win in three sets, 6-7 (4/7), 6-0, 6-2.
Zverev beat Federer at the Hopman Cup last year and came out all guns blazing on Saturday in a high-intensity first set where both players produced moments of brilliance and each holding multiple break points.
Federer's frustration was obvious as the set slipped away, dropping his racquet after missing an easy volley and then launching a ball towards the roof.
However, he turned the match around by approaching the net more often and using drop shots to catch Zverev napping.
The frustration changed sides of the net as the German copped a code violation for an audible obscenity after disputing the chair umpire's decision to replay one of his serves during the second set.
Zverev's serve, and resolve, was broken in the third game of the third set and fittingly it was a Federer drop shot which sealed the win.
Kerber, who is ranked 21st after starting last year at number one, then maintained her perfect singles record during the event to beat Bencic 6-4, 6-1 to level the tie.
Bencic, who was ranked seventh in the world before injuries stalled her progress, started brightly but Kerber soon took control and raced through the second set with breaks in the fourth and sixth games.
That set the scene for the mixed doubles, where Bencic produced some stunning returns on the Zverev serve and teamed superbly with Federer to claim the title with an emphatic 4-3 (5/3), 4-2 win under the Fast4 format.