In a blood and thunder affair Chester had seven players booked but defended well throughout to secure three precious points in their promotion push. But despite Chester's stubborn resistance the defeat was rough justice on an Orient side who twice rattled the woodwork as they dominated the game from start to finish.
But the O's could not find a way past Chester keeper Chris MacKenzie who pulled off a string of fine saves in a five-star show.
Chester looked dangerous on the break and carved out the first real chance and Orient keeper Glyn Garner tipped away a shot from the ever-dangerous Marcus Richardson.
However the home side quickly stepped up the pace and took a vice like grip on the game as Craig Easton and Michael Simpson stamped their authority in midfield.
Orient threw men forward at every opportunity as they carved out a catalogue of first half chances and topscorer Gary Alexander twice went close early on.
As the pressure mounted Joe Keith rounded off a superb move by firing an effort against the inside of a post - but the ball bounced to safety.
City keeper MacKenzie then saved well from Shane Tudor, Donny Barnard and Jabo Ibehre before Chester struck a deadly blow on the stroke of half time.
A well-worked corner on the left saw Drummond lose his marker and head home from close range.
After the break Orient hit the post again when Craig Easton fired in a shot and the ever alert MacKenzie denied Alexander's follow up effort.
Alexander was again denied by the keeper and Ibehre fired over as the home side continued to press.
Then sub Daryl McMahon went close with a shot and in a drama drenched finale that included six minutes of stoppage time MacKenzie made a fine double save as he palmed away MaMahon's effort and then blocked Lee Steele's attempt.