Baudry pounced from close range on the hour to cancel out Ethan Ebanks-Landell's fifth minute opener in front of a crowd of 28,598.
But Wolves should really have made the game safe well before Baudry scored with Orient's first shot on target as they squandered a host of chances.
Kenny Jackett's side made the perfect start when Ebanks-Landell surged forward from defence and picked up a pass from Kevin McDonald before rifling a shot past Jake Larkins from the edge of the area.
Wolves then dominated the first-half only for Jake Cassidy to waste two excellent chances while a last-ditch challenge from Baudry denied Michael Jacobs what looked to be a certain goal.
Kevin McDonald then shot weakly at Larkins at the start of the second-half and Baudry almost inevitably made Wolves pay for their failings in front of goal.
He ghosted into the area to stab home a right-wing cross from Moses Odubajo to ensure that honours were even in an entertaining encounter.