Williams – one of the Saddlers' 13 summer signings – found the net after just five minutes with a cool finish on the turn.
Michael Flynn, who again had a look at five trialists, then saw his side concede towards the end as the non-league Brakes equalised through Dan Turner.
Walsall fielded much-changed line-ups in each half, with Williams the standout performer during the first 45 minutes at the New Windmill Ground.
The former Cheltenham Town man was at the heart of their best moments going forward before going off at the interval.
Young playmaker Ronan Maher was among the several players to come on after the break and twice hit the woodwork.
The Saddlers struggled to put together a free-flowing performance against the Brakes, but it is no huge surprise with so many new faces through the door.
Walsall brought Flynn Clarke straight into the side after snapping him up on a season-long loan from Dean Smith's Norwich City.
He was operating in the playmaker role just behind Douglas James-Taylor and Williams – and the latter immediately made his mark.
Only five minutes were on the clock when the veteran frontman expertly picked out the bottom corner.
One of the Saddlers' trialists, ex-Newport County midfielder Aneurin Livermore made space and sprayed the ball wide to Hayden White. The right-wing-back then went on a marauding run before drilling a clever pass to Williams, who finished superbly on the swivel.
His instinctive, curling effort from the edge of the area left Leamington keeper Jake Weaver with no chance of making the save.
Williams, who turns 36 next month, continued to use his nous to his advantage.
Another bright moment in the first half saw him delicately control a lofted through-ball from Cameron Green – the former Wrexham full-back being another one of the players on trial – before seeing a half-volley tipped over by Weaver.
New-boy Flynn Clarke showed some silky skills while Livermore also showed some quality early on.
In the relentless heat, however, the pitch was noticeably dry, and Walsall did get into some bother when trying to play out from the back.
A few stray balls from the Saddlers' three-man defence of Donervon Daniels, Peter Clarke and trialist Ben Richards-Everton offered Leamington some half-chances. Simeon Maye saw an attempt from the edge of the area comfortably gathered by Owen Evans.
The hosts' best opportunity before the interval saw skipper Jack Edwards head wide of the far post.
Flynn freshened things up after the break as seven players came on for the beginning of the second half.
Adam Przybek, Liam Bennett, Manny Monthe, Liam Kinsella, Taylor Allen, Maher and trialist striker Timmy Abraham entered the fray.
Allen almost got himself on the scoresheet shortly after being introduced, too, as his near-post header was parried wide by Weaver.
Monthe soon guided another header narrowly off target from an unmarked position – an opening he should have capitalised upon.
Walsall had also changed to a a 4-5-1 system, and they looked a bit more cohesive thanks to that switch.
Kinsella, having taken the armband from Daniels, helped increase the tempo in the middle of the park while Abraham – the younger brother of England and Roma star Tammy – was keen to stretch the Brakes' defence with his pace.
Academy product Maher caught the eye in a brief cameo against Villa at the weekend and was keen to make the most of his minutes against Leamington as well.
He tried his luck from 20 yards out but saw his well-struck shot kiss the post.
As the clash approached the closing stages, the Saddlers began to offer less in attack and were eventually pegged back.
Leamington went close from a corner as a goalmouth scramble saw the ball cannon off the woodwork before flying out for another corner.
Walsall, ultimately, did not heed the warning as the second delivery was headed across goal and left Turner with a simple tap-in from a couple of yards.
Teenager Maher – the Saddlers' bright spark during the second period – did his best to win it in style for the Saddlers but saw his gorgeous half-volley glance the bar on its way over.
A good workout, although Flynn will be disappointed with the nature of the equaliser.
Walsall's next stop in pre-season is at Leamington's National League North rivals AFC Telford United on Saturday.
Leamington (4-4-2): Weaver; Meredith, Streete, Lane, Kelly-Evans; Cook (Trialist B, 65), Prosser, Maye (English, 56), Trialist A (Walker, 43); Turner, Edwards (c) (Trialist C, 77)
Subs not used: Naylor, Day
Goal: Turner (78)
Walsall (3-5-2): Evans (Przybek, 46); Daniels (Bennett, 46), P Clarke (Monthe, 46), Richards-Everton; White (Kinsella, 46), Comley (Allen, 46), Livermore, F Clarke (Mukuna, 71), Green; Williams (Maher, 46), James-Taylor (Abraham, 46)
Subs not used: Riley, Kiernan, Hutchinson, Menayese
Goal: Williams (5)