A first half corner count of 9-1 to Leeds reflected their superiority. But they were denied a breakthrough by fine saves by Orient keeper Jamie Jones from Gary McSheffrey and Leigh Bromby.
Orient, by contrast, were restricted to token efforts by midfielders Sean Thornton and Jason Demetriou which posed no problems for United keeper Casper Ankergren.
Leeds maintained the relentless pressure after the break, while Orient replaced leading scorer Scott McGleish with the greater physical presence of French substitute Jonathan Tehoue.
The home side came more into the game during the closing 25 minutes and won several corners, and centre-back Tamika Mkandawire was on hand to head home a cross from the left by Nicky Adams for his sixth goal of the season eight minutes from time.
But just when it seemed the Londoners had gained a remarkable win, Daniels turned the ball into his own net in stoppage time following Luciano Becchio's shot.