They are well placed to mount a promotion bid for the second successive season and manager Richard Money was delighted with the performance.
He said: "The conditions were so bad that on one occasion in the first half my goalkeeper Clayton Ince saw his clearance blow back for a corner.
"The weather improved in the second half and we got the ball down and played some good stuff."
Yeovil had three players suspended and loanees Lee Peltier and Darren Way recalled by Liverpool and Swansea respectively, but their new-look team attacked incessantly and should have scored early on.
James Walker missed an early chance and heroic defending blocked numerous Yeovil attacks. although they should have scored.
"I counted four chances in the first five minutes and 12 in all," said bitterly disappointed Glovers boss Russell Slade.
Walsall came out for the second half and were still under pressure for a time, but again their defence did its stuff.
They got the breakthrough they needed on 57 minutes. Michael Ricketts, the experienced striker who had been a doubt before the game, went off injured but his replacement Richard Taundry set up the goal with his first touch.
He knocked a free kick into the goalmouth and centre-half Scott Dann back-headed into the roof of the net.
Six minutes later the Saddlers got the clincher. Alex Nicholls, outstanding on the left side of midfield, brushed past his marker into the box and fired a low shot past home keeper Steve Mildenhall.