After the visitors had gone close through Craig Easton, it was Scunthorpe that opened the scoring in the sixth minute.
The Orient defence was nowhere to be seen as an unmarked Sharp raced into the box to turn a cross from Dave Mulligan past goalkeeper Glyn Garner from close range.
But the visitors were back on level terms just four minutes later when Easton this time did find the back of the net with a diving header from a right-wing cross by former Iron loanee Peter Till.
For a spell the Londoners threatened to turn the form-book upside down. But Scunthorpe finally settled after midfield man Matt Sparrow fired them back in front in the 38th minute with a low shot from the edge of the box.
Sharp then struck again to put the result beyond doubt in the 57th minute when he broke away down the right and fired a terrific right-foot shot past Garner.
Orient knew it was not to be their day when skipper John Mackie thundered a header against the bar from a corner by Matt Lockwood.
In the closing stages though it was Scunthorpe that might have doubled their tally. They too were denied by the woodwork when a fierce right-foot shot from Andy Keogh crashed back off the underside of the bar.
Goalkeeper Garner then rescued his side with a full-length save to turn away a rasping right-foot shot from winger Cleveland Taylor.
And it was Garner again to the rescue when he somehow managed to turn away a brilliant ten-yard volley from substitute Steve Torpey.
It was Orient's seventh away defeat of the season while in-form Scunthorpe march on having taken 22 points from the last 27.