But Nigel Adkins' team needed to come from behind after Crewe's own hot-shot Luke Varney broke the boredom of a dull opening spell by finishing off a well-worked move for an opening goal in the 26th minute.
When Ryan Lowe banged the ball to the far post, Varney saw his header palmed away by Joe Murphy. Michael Higdon returned the ball back to him and he finished the chance with ease.
Crewe's lead lasted just three minutes and it was lethal finisher Sharp on target again when David Mulligan crossed the ball into the box.
Two defenders missed their clearances allowing Sharp the opportunity to volley into the corner at close range.
Sharp's strike partner Jermaine Beckford produced an even better finish five minutes before the interval.
The on-loan Leeds United youngster cut in from the right and hit a dipping shot over home keeper Ben Williams.
Cleveland Taylor also went close as Scunthorpe finished the half the stronger side.
It was still a fairly tight contest when Crewe wasted a chance to equalise on the hour-mark. Lowe smacked the ball over from 15 yards when Varney pulled it back across the box.
It proved to be a crucial miss as Scunthorpe went back up the other end within a minute for Sharp to head in Matthew Sparrow's cross from close range to finish the game off.
The visitors could have added more in the closing stages with Beckford being denied at the near post by Williams.