In bitterly cold conditions, Clarke took his tally for the season to 12 goals when he collected a pass from Mat Sadler on the edge of the box, turned and curled a superb shot over goalkeeper Jamie Jones and into the roof of the net after 11 minutes.
It was an advantage they nearly doubled soon afterwards when the dangerous Nicky Adams sent in a cross from the left that was met by Mike Jones but his header from 10 yards hit the crossbar and bounced over.
Clarke might have added another goal when he pounced on a flick on by Orient defender Mathieu Baudry but snatched his shot hopelessly wide of the target.
Lacklustre Orient raised their game after the interval, although there was little to trouble Town keeper Paul Jones. However, he did well to keep out a close-range header form Dean Cox with 10 minutes remaining.