One hundred years, almost to the day, after winning the first grand slam, Wales won their tenth and the euphoria will sustain the country's power supplies for weeks. The transformation in fortunes, not only since the World Cup last September but from a dire first half against England at Twickenham on the first day of this RBS Six Nations Championship, has been remarkable and heart-warming.

The Millennium Stadium in Cardiff on Saturday gave the tournament everything a climax should be: a passionate atmosphere, two teams playing to the edge of their powers, but above all a clarity of purpose and execution lacking from their four rivals. For an hour of this 29-12 victory for the Welsh, France played as well as the home side, reminiscent in some ways of how Toulouse played against London Wasps in the Heineken Cup final of 2004; the French lost that one, too, against a team prepared by Warren Gatland and Shaun Edwards.

What have those two coaches brought with them? “Clarity, structure, intensity,” Shane Williams, the hero of the hour and of the championship, said. “Honesty, respect, workrate,” Alun-Wyn Jones said. The mixture of New Zealand, the North of England and, lest it be forgotten, the innate Welsh understanding of Rob Howley and Robin McBryde, have pulled a disparate collection of talents up by their boot strings and made them kings of Europe.

Two moments that stand out: the try by Williams, his 41st, which makes him Wales' leading tryscorer and was his sixth of this championship. The score was 9-9, the converted try made it 16-9: would France respond or break? They responded, but the try had added stature to every Wales player. “No matter how tired you are, you pull your mate off the floor and drag him around with you,” Ian Gough, who won his 50th cap, said.

The second moment came after an uncharacteristic defensive dither between Stephen Jones and Lee Byrne that gave France, trailing by ten points, an attacking scrum ten metres out. Wales put down an eight-man drive, France reeled and the ball was turned over. It was a massive statement from a pack that, before this year, had not frightened many but now possesses the conviction that it can hold its own against anyone.

At that moment, Wales must have known that they would win. It had not always been so against a France team who had been selected to defend their title, in contrast to the endless examination of potential that Marc Lièvremont, their coach, has undertaken this year and that, on Saturday, left good players underprepared in terms of cohesion and understanding.

Julien Malzieu and Fulgence Ouedraogo, one a wing the other a flanker, have powers of acceleration that will be wonderful weapons for France in the future, while Ouedraogo is an athletic lineout presence, too. He was the recipient of the high tackle from Gavin Henson that earned the centre a yellow card, but in his absence Wales held firm - helped by brainless play from David Skrela, who hoofed away possession at a time when Wales effectively had only 13 players on the pitch, with Henson in the sin-bin and Gethin Jenkins receiving treatment.

But Wales never lost their purpose, even though Jean-Baptiste Elissalde's third penalty goal brought France level during Henson's absence. He and Tom Shanklin give so much stability to the back line that when Wales err, they always have a fall-back position, which usually involves Martyn Williams, whose reading of the game has been so vital to this grand slam.

If the first hour was a fencing match, the last quarter was a riot of colour. The defence prepared by Edwards has led directly to tries in the championship, notably against England; here the line speed as France went wide behind a scrum on their own ten-metre line forced the wayward pass from Skrela that Yannick Jauzion had to pluck from behind him and the ball went down.

Shane Williams was on to it in a flash, kicking through and then away from the desperate cover and beating Anthony Floch to the touchdown. Stephen Jones added the conversion and a 38-metre penalty goal, showing a different kind of strength to that of James Hook, whose kicking had given Wales their slim first-half advantage.

Dimitri Yachvili recovered three points, nullified three minutes later by Stephen Jones's second goal, but the glory of Wales was still to come. Alun-Wyn Jones swept on to a France knock-on in the Wales 22 and Mark Jones cut such a wonderful angle that he was through the first line of defence before France knew it, with 70 metres ahead. Malzieu and Cédric Heymans hauled him down a metre short of what would have been the try of the tournament, but the damage was done.

Wales patiently worked their way to a ruck just inside the France 22 and Martyn Williams suddenly found a hole and galloped over for the second try. This was the man Gatland talked back into international rugby after he had announced his retirement, which speaks volumes for the New Zealander's persuasive powers. He told his players when he arrived that they had to have a dream; he, and they, have made the dream come true.

Scorers: Wales: Tries: S Williams (60min), M Williams (77). Conversions: S Jones 2. Penalty goals: Hook 3 (8, 19, 22), S Jones 2 (64, 74). France: Penalty goals: Elissalde 3 (20, 40+2, 47), Yachvili (71).

Scoring sequence (Wales first): 3-0, 6-0, 6-3, 9-3, 9-6 (half-time), 9-9, 16-9, 19-9, 19-12, 22-12, 29-12.

Wales: L Byrne (Ospreys); M Jones (Llanelli Scarlets), T Shanklin (Cardiff Blues), G Henson (Ospreys; sin-bin, 40+2-50), S Williams (Ospreys); J Hook (Ospreys; rep: S Jones, Llanelli Scarlets, 56), M Phillips (Ospreys); G Jenkins (Cardiff Blues; rep: D Jones, Ospreys, 49-53) H Bennett (Ospreys; rep: M Rees, Llanelli Scarlets, 56), A Jones (Ospreys; rep: D Jones, 71), I Gough (Ospreys; rep: I Evans, Ospreys, 71), A-W Jones (Ospreys), J Thomas (Ospreys), M Williams (Cardiff Blues), R Jones (Ospreys).

France: A Floch (Clermont Auvergne; rep: C Heymans, Toulouse, 67); V Clerc (Toulouse), Y Jauzion (Toulouse), D Traille (Biarritz), J Malzieu (Clermont Auvergne); D Skrela (Stade Français; rep: F Trinh-Duc, Montpellier, 63), J-B Elissalde (Toulouse; rep: D Yachvili, Biarritz, 63); F Barcella (Auch), D Szarzewski (Stade Français; rep: W Servat, Toulouse, 44), N Mas (Perpignan; rep: J-B Poux, Toulouse, 61), L Nallet (Castres), J Thion (Biarritz; rep: A Mela, Albi, 75), T Dusautoir (Toulouse), F Ouedraogo (Montpellier; rep: E Vermeulen, Clermont Auvergne, 61), J Bonnaire (Clermont Auvergne).

Referee: M Jonker (South Africa).

Attendance: 74,609.