The duo won their singles rubbers to secure the A$1 million mixed team title at the expense of the United States.
Hingis, 20, showed why she is favourite for the Australian Open with another impressive display in beating world number four and new doubles partner, Monica Seles, 7-5 6-4 in the women's singles rubber.
Switzerland, who secured the Hopman Cup for the first time in 1992, were assured of another victory when Federer, the 19-year-old rising star, proved too strong for Jan-Michael Gambill and won 6-4 6-3.
That gave Switzerland an unassailable 2-0 lead in the best-of-three rubbers tie, before the US regained some pride with a 2-6 6-4 7-6 (7-5) win in the mixed doubles.
It was the fourth time that Hingis had appeared at the Hopman Cup and she had failed on the previous three occasions in 1995, 1996 and 1999.
Her disappointment was acute in 1996, when she and partner Marc Rosset reached the final only for their victory bid to backfire at the worst possible time.
With the tie level 1-1 and the decisive mixed doubles rubber against Croatia locked at 5-5 in the final set, Rosset punched an advertising hoarding in a burst of anger.
He broke his hand and the Swiss had to default - presenting the title to Croatia.
WATCHING LIKE A HAWK
"After what happened five years ago, I was watching Roger like a hawk all week," said Hingis.
"I told him not to get into trouble and not to do anything stupid, because I didn't want to have to go through that disappointment again.
"But everything went very well in the end - Roger was a great partner and I think we deserved to win."
Hingis took her win-loss record against Seles to 13-2 with her 72-minute victory.
She broke the 27-year-old former world number one three times in the first set, and at 4-4 in the second, Hingis pounced to claim the only break point she carved out in the set.
She served out for the match - her 14th consecutive Hopman Cup singles victory - and said: "I have a good record against Monica, but with a player as good as she is, you know it can go either way at any time.
"But I am very happy with the way I played, and it is a great start to another important season for me.
"I hope this form continues throughout the Australian Open - but I keep saying that I can get even better."
Hingis and Seles will play doubles together at the Sydney International event from January 8, and at the Australian Open, which begins in Melbourne on January 15.
SELES DENIED
The outcome denied Seles the chance to become the first player to win the Hopman Cup twice. She won her first with her native Yugoslavia in 1991, partnering Goran Prpic.
Federer, whose best ATP Tour performance to date was a runners-up place in Basle last year, claimed his first career title with the victory.
There are no ranking points available because the Hopman Cup is recognised only as an International Tennis Federation (ITF) event.
But Federer said: "I was a guest of the Switzerland team at the Hopman Cup two years ago, and I thought then what an honour it would be to play with Martina for real.
"It feels great now that I have achieved that goal, and it sets up the season for me very well. I feel this is going to be a big year for me.
Hingis and Federer shared a cheque for A$240,000, and each also received a diamond-encrusted tennis ball worth A$35,000.