Legzdins again came to his side's rescue when he made a point-blank save before diving at the feet of Jamie Proctor.
Henderson was not to be denied a second time, however, and powered a header home to put his side in the lead following good work from Jobi McAnuff.
After the break, Baudry blocked a Steven Scumacher drive before Romain Vincelot almost broke away following a couple of mistakes from the Fleetwood defence.
Proctor thought that he had equalised for Fleetwood after putting in the rebound from David Ball's blocked shot, but the flag went up for offside.
At the other end, Orient hit the bar for a second time. This time it was Mooney, who headed against the woodwork after getting onto the end of Cox's cross from the left.
They were made to rue the missed chances as Dobbie put Fleetwood on level terms by latching onto a loose ball and slotting home.
Mooney then had a great chance to steal his side all three points after Cox played him in, but he bent his effort high and wide, meaning that both sides had to settle for a 1-1 draw.body check tags ::