Both teams spurned a host of good opportunities as the Somerset outfit extended their disappointing recent run to five games without a win.
The sides exchanged early blows with towering defender Dan Burn heading narrowly wide, before Febian Brandy's powerful strike was palmed away by Glovers goalkeeper Marek Stech.
The Saddlers gradually took control as the half developed and came closest to breaking the deadlock when Jamie Paterson smartly cut in from the left and unleashed a swirling strike which curled agonisingly wide of the post.
The visitors, who are now unbeaten in their last 11 League One games, continued to threaten with Brandy and Paterson's trickery down the flanks keeping the Huish Park faithful on edge.
Yeovil struggled to offer any service to League One top scorer Paddy Madden and were left further frustrated when referee Tim Robinson turned down a penalty appeal when James Hayter clashed with Paul Downing.
Walsall came close to snatching the spoils when in-form Will Grigg shot over from close range, before Craig Westcarr missed a glorious header from three yards out.