In recent races Hill has made poor starts but this time it was Villeneuve's turn to wheelspin when the race finally got underway following a delay when David Coulthard's McLaren-Mercedes stalled just before the green lights came on. That necessitated a further grid formation lap, but Hill kept his nerve and, as Villeneuve faltered, he took a lead he was never to lose.
When he took the chequered flag after the most important hour and 32 minutes of his life, Hill led Michael Schumacher and Mika Hakkinen home to score his 21st grand prix victory, his eighth of the season, and made history by becoming the first son of a world champion to emulate his father's achievement.
Drenched in champagne, Hill said: "It's a lot to take on board, really. It takes up a lot of your mental energy just doing a grand prix. When you've won the world championship and the grand prix all in one race, it's a hell of a thing. This is going to take a while for the full impact to hit me, but right now I feel like I'm on a rocket that's just taken off. It's just a wonderful relief of pressure and sense of satisfaction.
"The chequered flag was a beautiful moment, and then I was allowed to let go and start to congratulate myself without having to concentrate on what I was doing."
Before the race Villeneuve's confident pole position had thrown the outcome of the title fight into doubt, but Hill regained his momentum when it mattered and stamped his authority from the outset. By the 12th lap Villeneuve had recovered to fourth place, behind Hakkinen and Schumacher, after overtaking Eddie Irvine's Ferrari. The gap between the two Williams-Renault drivers was never more than nine seconds, apart from during their refuelling stops, but Hill was in full control.
"I felt great when I saw Jacques' start," he admitted, "but I also felt great at Monza, so I was just out there at the front, thinking: 'This is all very well, Hill. Stay calm, and see it through to the finish. Just drive nice and easy.' And that's all I did all race. I kept a good enough advantage over Michael and Mika."
On the 31st lap Villeneuve radioed his pit to say that he suspected he had a puncture, but while the team was examining the tyres he discarded at his second pit stop on lap 32, and finding no such evidence, the Canadian radioed again to say that his car was still handling oddly. Just as he started his 37th lap, still running in fourth place well behind Hill, he discovered why. His car twitched, slid off the road into a sand trap, and was overtaken by its own right rear wheel which had worked loose. Fortunately the errant wheel was restrained by the second layer of safety fence, but Villeneuve's bold challenge was over. Bitterly disappointed, the Canadian was none the less magnanimous in defeat.
"Damon did a great job," he said. "He's driven superbly all season, better than ever, and he is a worthy champion."
Hill was now home and free, though the news of Villeneuve's demise was a mixed blessing. "Fifteen laps from the end I got the message he was out," he said. "But try and concentrate on the race when you realise you're world champion. If I'd reacted to that then I would have taken my eye off the ball. It was a matter of just trying to put it out of my mind, if you can believe it, because the next job was to win the race and I really, really wanted to do that. The win was for the team, but the championship was for me."
His one moment of drama during what he described as a perfect race came on the third lap, when Gerhard Berger tried to pass him in the chicane at the end of the lap. This ridiculously tight corner is the only place where overtaking is possible at Suzuka, and is infamous as the scene of the collision between Ayrton Senna and Alain Prost in 1989.
"I heard an engine noise - the first time I've heard one like that since I raced motorbikes - and I looked in my mirror and couldn't see him," Hill said. "Then when I looked again he was a long way back, so I don't know whether he took a big dive at me... I just took my line."
Berger, who had tried an audacious move, was not impressed. "I'm sure he can't have seen me, otherwise he'd never have come across like that and risked so much. He has me to thank for championship, because I had to drive off the road to avoid hitting him."
The incident delayed the Austrian, who might otherwise have won the race. As he fought back to fourth place he was later involved in a second incident at the chicane which saw Irvine pushed into retirement.
Still on a high, Hill added: "I think I'm going to celebrate at least until Christmas, maybe a little beyond that. You know, it could have gone the other way. I might have been standing here and Jacques could have been champion and I would have been feeling pretty sick, but I know Jacques is going to get another chance. He's young and he's quick and, to be honest, it had to be this year for me."
Frank Williams, who Hill rather pointedly omitted from the list of people he thanked publicly afterwards, said: "In many ways it's more appropriate for Damon to win, because he has worked hard for four years. He's climbed the mountain, and he's now at the top. He deserves to be there."
At Suzuka yesterday, Damon Hill laid to rest the old adage that the good guys never win, and he did it with style.