Effort far outweighed quality in the dull opening stages before Vale twice went close to taking a 29th-minute lead.
Gary Woods saved a 30-yard drive from Ryan McGivern and the Orient goalkeeper then deflected Chris Lines’ shot against a post.
But the O’s were really up against it a minute later when Henderson was shown a straight red card for elbowing Vale defender Richard Duffy.
The visitors survived increasing pressure as half-time approached and Vale striker Jordan Slew had a header ruled out for offside seconds before the interval.
Orient’s 10-men continued to hold firm in the opening stages of the second half, before Rob Page’s team took control with two goals in the space of three minutes.
Right-back Adam Yates broke the deadlock in the 63rd minute, firing a right-foot shot into the top right-hand corner of the net from 15 yards after he was set up by Mark Marshall.
And Ben Williamson drove an angled right-foot drive from 12 yards into almost the same spot after he spun onto a pass from Michael O’Connor.
Nathan Clarke deflected a free-kick from O’Connor into his own net in the 81st minute to complete Orient’s misery.
Breaking news, transfer gossip, line ups and goal alerts from your football club – delivered direct to your mobile. Sign up for Sky Sports Alerts