The hosting Blades had the chance to break the deadlock within the opening 60 seconds, but Jose Baxter failed to find the target when well placed.
From that moment onwards, chances were few and far between, although it was United that dominated proceedings.
However, despite that domination, it was Orient that broke the deadlock seven minutes before the break. Alex Pritchard sent the ball across the face of goal and Simpson was on hand to score from close range.
Then, 60 seconds later, Orient winger Jobi McAnuff fired in a dangerous shot that flew inches wide of the upright as the visitors ended the half brightly.