Nathan Clarke struck a 79th-minute equaliser for the Londoners to cancel out Paul Downing's first-half strike, but the O's slip four points behind second-placed Brentford in the race to the Championship.
The Saddlers started much the better of the two sides and would have gone ahead inside 10 minutes if not for the intervention of goalkeeper Eldin Jakupovic, who tipped Milan Lalkovic's goal-bound effort onto the woodwork.
However, Dean Smith's men took the lead on 14 minutes through Downing, who capitalised on Orient's failure to clear from a corner to smash a loose ball home from close range.
Slade's side forced the issue in the second half and drew level with 11 minutes of normal time remaining through Clarke, whose speculative effort took a big deflection and looped over Richard O'Donnell.
Orient pushed for a winner in the closing stages, but Walsall held on for the point.