On a difficult pitch with surface water and heavy rain falling for much of the game, it took the O's just seven minutes to move in front when Moses Odubajo seized on to a defence-splitting pass from Dean Cox and slid the ball through the legs of advancing goalkeeper Alan Davies.
Kevin Lisbie missed a penalty in the 27th minute after being hauled down by Chuks Aneke, the striker sending his spot-kick wide of the target.
The hosts were awarded another penalty 10 minutes later when David Mooney was brought down by George Ray, but this time the O's striker slotted the ball neatly home.
The visitors had their backs to the wall throughout the first 45 minutes, but did show more as an attacking force after the break winning 11 corners, while Aneke twice went close.
He saw a header finger-tipped over the crossbar by Jamie Jones and then beat the O's goalkeeper only to see his shot crash against the woodwork and rebound to safety.
But the resolute Orient defence held firm to make it four wins out of four league matches and move back to the top of the table.