Holmes curled in an exquisite 11th minute free-kick after Kevin Betsy had been fouled 22 yards out by Jerel Ifil and the Saddlers midfielder effectively sealed the points with a second on 56 minutes.
Swindon were never in contention and were rattled from the very first minute when Walsall veteran striker Tommy Mooney had a headed effort ruled out for offside.
That seemed to unsettle the Swindon defence and their hesitancy was there to see as Ifil found Betsy to provide Holmes with the opportunity to put Walsall ahead.
In contrast Walsall keeper Clayton Ince enjoyed one of his quietest afternoons and Swindon strikers Simon Cox and Billy Paynter received no change from Saddlers defenders Ian Roper and Anthony Gerrard.
Town enjoyed a spell of pressure at the start of the second half, but Ince was untested and Walsall deservedly doubled their lead when Holmes latched on to Mark Bradley's pass.
Although his initial effort was saved by Phil Smith, the Walsall midfielder reacted first to the loose ball to score.
Cox denied Holmes a hat-trick with a last-ditch tackle, but was lucky to escape with a yellow card for a late challenge which saw Bradley stretchered off.
As Swindon's fans streamed out of the ground Walsall rounded off their afternoon when Betsy took advantage of another defensive lapse and, although Smith again saved his effort, the luckless Swindon keeper could only watch as Alex Nicholls drilled the loose ball into an unguarded net.
Ince was at last forced into action in injury time as he tipped over a defiant parting shot from Paynter, but it was not enough to stop this disgruntled home supporters from booing the Robins off at the final whistle.