Rugby lifted themselves back out of the relegation zone with a convincing victory at Butlin Road.
Liam Francis headed the hosts ahead after Walsall keeper Dale Eve had dropped Chris Clements's inswinging corner, with Loyiso Recci then doubling Town's lead from the spot after Mikey Taylor was pushed down in the box.
The one-sided first-half continued and both Ryan Sahota and Theo Rowe went close for Valley, although Recci also did well thwart Ross Evans just ahead of the break.
It was a more even affair after the restart, and Dan Summerfield was soon blocking Wood's Charlie Mansell's goalbound effort, before Recci made the game safe on 83 minutes with another penalty after Sahota had been fouled.
Silvano Obeng added Rugby's fourth shortly after when he followed up on Eve's parry to Sahota's strike.
