He was a runaway choice as man of the match in his second appearance of the tournament finishing with a hat-trick and very nearly a fourth try only to have it contentiously over-ruled by the video referee.
The tries were just the icing, though, as SBW produced a virtuosso performance, especially in the first half when the Kiwis surged to a 40-0 lead.
The New Zealanders wouldnt be as pleased with their second half effort when changes to the combination resulted in a stuttering display which produced just 16 points while Papua New Guinea lifted its energy levels with two tries.
Williams reflected feelings inside the camp immediately after the game when he bemoaned the fall-off in the Kiwis standards. In fairness, though, some significant line-up shuffles didnt help.
First Thomas Leuluai, coming on at halftime, lasted only a few minutes before being forced off with more groin trouble after the Kumuls had scored early in the second half. His quick exit meant Shaun Johnson was no sooner off than he was back on again. Wing Manu Vatuvei, outstanding in the first half, seemed to be troubled by his ankle injury, too; in his absence centre Bryson Goodwin was moved to the left wing and second rower Alex Glenn to the centres. With just two bench players the interchange balance and options were severely affected.
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Earlier on, though, the Kiwis were exceptional as they opened the Kumuls up at will in scoring seven first half tries.
In the opening 40 alone Williams' stats were astonishing: 13 runs, 101 metres, eight tackle breaks, six off loads, four line breaks and a try assist as well as his three tries. He didnt see anywhere near as much play in the second half as the Kumuls enjoyed a greater share of possession but he still finished with 158 metres from 20 carries.
The Kiwis tries started flowing just three minutes into the contest when Goodwin raced onto a Kieran Foran grubber before quickstepping winger Roger Tuivasa-Sheck scored a double in the space of four minutes. His deed was followed by SBWs first two tries, another to Frank-Paul Nuuausala (off a Williams off load) and then SBWs third right on halftime.
Throughout the half the New Zealanders had the ball zinging all over the park although the attack was largely aimed at the right side.
While he didnt see much in the way of try-scoring opportunities, Vatuvei didnt want for work as he tore off an impressive 107 metres from seven runs.
The right side again paid dividends in the second half as Johnson and Foran combined to give centre Dean Whare a double while Elijah Taylor scored the 10th and final trial wide out on the left picking up the scraps after a Johnson bomb.
Papua New Guinea unquestionably had the big local crowds support, roaring with delight when a last tackle shift ended in a try for halfback Dion Aiye. The Kumuls also finished the nights scoring with a superb long-range strike finished by the exotically named Wellington Albert. The fans couldnt have been more delighted.
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The Kiwis, though, were more concerned about their display as they eye the quarter-finals and a match-up next week against either Scotland or Italy.
Williams aside plenty of the forwards enjoyed profitable nights. Prop Jesse Bromwich ran a game-high 172 metres from 19 carries, Vodafone Warrior Ben Matulino 121 metres from 14 runs, hooker Issac Luke 166 from 15 and interchange props Sam Moa and Sam Kasiano 114 from 13 and 109 from 13 respectively.
Johnson and Foran directed things nicely with six try assists between them while out wide Tuivasa-Sheck made 114 metres from 14 runs, six tackle breaks and two line breaks and Whare made 108 metres from 10 runs plus two line breaks and two line break assists.
With 16 points from eight conversions, Johnson has scored 50 points in three games so far.
The Kiwis are back at Headingley for their quarter-final next Saturday morning (NZT).
At Headingley, Leeds
New Zealand Kiwis 56 (Sonny Bill Williams 3, Roger Tuivasa-Sheck 2, Dean Whare 2, Bryson Goodwin, Frank-Paul Nuuausala, Elijah Taylor tries; Shaun Johnson 8 conversions).
Papua New Guinea Kumuls 10 (Dion Aiye, Wellington Albert tries; Francis Paniu conversion).
Halftime: 40-0 Kiwis.
Referee: Ashley Klein (Australia).
Kiwis: Josh Hoffman; Roger Tuivasa-Sheck, Dean Whare, Bryson Goodwin, Manu Vatuvei; Kieran Foran (c), Shaun Johnson; Ben Matulino, Issac Luke, Jesse Bromwich; Alex Glenn, Sonny Bill Williams; Elijah Taylor. Interchange: Sam Moa, Sam Kasiano, Frank-Paul Nuuausala, Thomas Leuluai.
Kumuls: David Mead; Josiah Abavu, Emmanuel Yere, Francis Pamiu, Nene McDonald; Ray Thompson, Dion Aiye; Neville Costigan, Charlie Wabo, Joe Bruno; Jessie Joe Nandye, Jason Chan; Sebastian Pandia. Interchange: Wellington Albert, Paul Aiton, Jason Tali, Mark Mexico.