Saints were ahead early from a Mark Percival penalty awarded perhaps harshly, but for a nonetheless silly push in the back by Zane Musgrove.
But Sneyd conjured up a transformation on the scoreboard, sparked by the creative role he played in Wire’s opening try.
Running to the right across the park, he suddenly dinked a kick through with the outside of his left foot and, with Saints caught cold, Williams ran on to touch down his first Super League try of the season.
It was a piece of artistry that Saints assistant coach Lee Briers, once a Wire hero, would have appreciated,
New signing Sneyd added the extras, then a penalty to earn his side an 8-2 half-time lead. But, within eight minutes of the restart, it was back to all square again when Morgan Knowles bulldozed over to mark his 200th Super League appearance with a try and Percival landed the routine conversion.
Saints then shot themselves in the foot when they gifted Wire a second try.
Jack Welsby’s sloppy loose pass went badly astray, bounced kindly for Matty Ashton and the winger kept his cool to collect and run from deep inside his own half down the left flank and round in front of the posts. It was his sixth try against Saints in his five most recent meetings with them.
Saints were then back within two points when teenage winger Dayon Sambou marked his debut by diving spectacularly over in the left corner. But Percival shanked his conversion attempt, which fell short and wide.
And that proved to be the difference between the two sides, as Wire’s late territorial superiorty helped the visitors over the line and continue their stranglehold over Saints in this fixture.