But optimism was quickly replaced by damage limitation as Wales scored two converted tries during the opening 12 minutes and then ran out 34-7 victors, with Scotland restricted to a late Peter Horne try that Finn Russell converted for their only scoring contribution.
Instead he passed directly behind him to Williams who, detecting that Scotland were narrow in defence, passed long to Leigh Halfpenny for the full-back to score his first global try since 2013.
Wales were patient in defence, though, and were gifted a try in the sixth minute when Gareth Davies intercepted a delayed pass from Ali Price and had the pace to beat the cover defence to score. A fine conversion from Leigh Halfpenny extended the lead to 7-0.
Scotland travelled to Principality Stadium with high hopes of beating an injury-hit Wales side, but it was instead on the end of a humbling defeat.
However, after a couple of offloads in the tackle nearly put through Alun Wyn Jones, his final pass to Steff Evans was knocked on and the chance was lost.
During last year's Six Nations, Scotland had ended a nine-game losing streak against Wales as two second-half tries clinched a 29-13 victory at Murrayfield. The conversion put the hosts out of sight at 27- 0 with twenty minutes to go.
After that whirlwind start, neither side could make any lasting inroads, with the ball going to ground too often and defenders scrambling well when required. They made the absence of eight Lions an irrelevance by splicing all the confidence and verve which had carried the Scarlets into the Champions Cup quarter-finals - and 10 of them started here - to the ferocious defensive upgrade installed by Shaun Edwards and the alchemy exposed Scotland's new-found confidence as a mirage. Halfpenny lined up an easy three points, and Scotland had a mountain to climb if they were to make a fight of the match.
Scotland then shot themselves in the foot early in the second half by giving penalties away on 43 and 48 minutes, which Halfpenny successfully struck to add yet more points to his tally.
Scotland continued to push and were desperate to turn their possession and territory into points.
But Halfpenny caught the ball when he found himself on the right wing moments later and raced over for a second quickfire try which he also converted. But Wales did add to their lead three minutes after the interval.
"There was no expectation against Scotland, ex-players and the media were saying we were going to lose and writing us off".
Scotland dominated the near half-hour to halftime but lapsed into error after error: Dropped passes, knock ons, a penalty kick not finding touch, crooked throw-ins, and the backs shuffling sideways to be easily contained by Wales.
Wales v Scotland is a fascinating opening match: Scottish coach Gregor Townsend oversaw a supreme set of performances in the autumn, including a 53-24 win over Australia - the first time in a decade that Scotland have scored over 50 points against anyone.
Evans dived over in the corner to finish the embarrassment for the visitors.