Williams opened the scoring three minutes before the break, after Jamille Matt had seen his goal disallowed earlier in the half.
Charlie Lakin took four minutes to open his goal scoring account with a classy volley into the bottom corner, before Jamie Jellis rounded off the win with a deflected finish on 84 minutes.
Walsall had two early chances to open the scoring when Josh Gordon glanced his header wide and Ronan Maher sent a looping volley onto the top of the crossbar.
Jamille Matt sent his header into the far bottom corner just past the quarter hour mark but saw his goal ruled out for a foul.
Alvechurch defender Callum Sullivan came close twice in quick succession when he header deflected off Harry Williams and crashed off the crossbar. Tommy Simkin was then called into action for the first time when the Stoke City loanee impressively clawed Crowther’s header to safety.
Liam Gordon began to combine with Donervon Daniels down the left towards the end of the first half and the Guyana international squared for Ryan Stirk to draw a strong save from Woods.
On the cusp of half-time, Williams marked his return to the Lye Meadow with the opening goal. Trialist A swung a dangerous cross into the penalty area, which both Josh Gordon and Matt were unable to send the ball goal bound.
The ball eventually ricocheted into the path of Williams and the defender kept his cool in front of goal to apply a composed finish past Woods.
As Walsall fielded an entirely different XI after the break, Charlie Lakin needed just four minutes to get off the mark for the club.
Taylor Allen hung his free-kick delivery to the back post as Oisin McEntee towered above his marker to cushion down for Lakin to score.
The Saddlers almost add a third with exactly the same free-kick routine as the last. Allen with another floated free-kick, McEntee with another knockdown but Trialist B was unable to find the target.
Trialist B had another chance to extend Walsall’s advantage when he cut inside and stung the palms of Woods with a ferocious effort.
Dylan Thomas, who was introduced midway into the second half, drilled a low volley straight down the throat of Woods, while Jellis dragged a low effort narrowly wide.
Jellis impressed in the second half and eventually capped his performance with a third as his low finish deflected beyond the reach of Woods six minutes from time after Walsall worked the ball inside from the right.
Thomas came close late on when he stabbed wide with a finish on the stretch at the near post and McEntee came even closer when Woods thwarted his diving header from Jellis’ sumptuous cross.
Walsall return to action on Wednesday night when they host Villa at Bescot with kick-off at
Teams
First Half XI (3-5-2): Simkin; Okagbue, Williams, Daniels (C); Trialist A, Earing, Stirk, Maher, L Gordon; Matt, J Gordon.
Second Half XI (3-5-2): G Barrett; McEntee, Farquharson, Allen; C Barrett, Jellis, Comley, Lakin, Weir; Trialist B, Wragg (Thomas 67).