The winger’s first was all Wales had to show for a dominant first half and the flawless kicking of Chris Paterson kept Scotland in the game even after James Hook had breached some sloppy Scotland defending to cross.

But Williams squeezed the ball in at the corner in the 68th minute to finally kill off the resistance of the visitors.

Scotland survived the early pressure though and took the lead through the boot of Paterson in the 10th minute.

Andy Henderson intercepted a pass from James Hook, allowing Paterson to kick towards the corner. Although he lacked the pace to reach it himself, Scotland won a penalty after the resulting lineout and Paterson, who kicked a perfect 17 efforts in the World Cup, made no mistake.

However, Wales were ahead three minutes later when Williams crossed after Hugo Southwell’s weak kick had gifted the hosts possession.

They worked the ball across to the left wing and Williams cut inside after a crucial burst from Lee Byrne, with Hook’s conversion making it 7-3.

Nathan Hines then marred his 50th cap by putting Scotland under needless extra pressure when he lashed out at Byrne with his elbow in full view of referee Bryce Lawrence, who brandished the yellow card.

The Scots survived their spell without Hines but Hook made it 10-3 with a 30th-minute penalty after John Barclay was penalised for holding on to the ball on the ground.

Scotland then lost skipper Jason White to injury with Allister Hogg coming off the bench. However, Paterson kept them in the hunt with a 40-metre penalty.

Paterson brought the visitors within a point with a straightforward penalty four minutes after the restart.

But Wales immediately took the initiative with a good passing move that looked to have fizzled out before Hook all too easily burst between Ross Ford and Euan Murray before crossing.

The Ospreys stand-off converted but Paterson made it four from four penalties after a good run from Ford to the 22-metre line.

And Paterson’s flawless kicking continued as he slotted over from 40 metres in the 56th minute following Ian Gough’s crude block on Henderson.

Wales made a flurry of changes and replacement Stephen Jones gave them some breathing space with a simple penalty in the 65th minute.

The home side continued to probe and the impressive Williams notched his second try three minutes later after brushing off two tackles.

The second, by his fellow Ospreys winger Nikki Walker, forced most of his body well off the park but the officials ruled he had touched down before his flailing legs went in touch.

Jones was accurate with the boot again and soon made it 30-15 with a penalty from the touchline.

Wales sub Sonny Parker was stopped in the corner before Scotland mounted a late challenge after Danielli had won a high ball but they could not force a consolation score.