The defeat, Orient's tenth at home, saw them slip back to the fringe of the relegation zone.
The home side were quick out of the box and, on six minutes, striker Scott McGleish saw a shot gathered at the second attempt by Walsall keeper Clayton Ince.
Simon Church then showed good awareness to get on the end of Chris Palmer's under hit back pass but, under pressure from Ince, he shot wide.
The lively Jimmy Smith, on loan from Chelsea, then set Church clear but his effort was again saved by the impressive Ince.
But gradually Walsall got a foothold in the game and started to turn the tide.
The danger signs were flashing for Orient when Sofiene Zaaboub saw a shot tipped over by Jamie Jones.
But, on the stroke of half time, Charlie Daniels gave possession away and Alex Nicholls, Jabo Ibehre and Troy Deaney were all involved in a slick move before Deeney's clever pass to Bradley split the home rearguard and he raced clear and fired into the top corner.
After the interval Orient tried hard to fight their way back into the contest and Smith saw his close-range effort tipped away by Ince, then McGleish shot just wide.
Orient boss Geraint Williams threw John Melligan and Wayne Gray into the fray in a bid to save the game.
But Walsall looked comfortable and it was the final ten minutes before Orient finally found a head of steam.
In a frantic finish Ince made excellent saves from Church and Jason Demetriou and then Daniels headed a corner over - but Walsall weathered the storm and hung on for a comfortable victory.