Only 11 minutes in and Town took the lead, Carchedi played a neat one-two with Ash Hildred on the edge of the box before slipping the ball underneat Kristian Rogers in the Blades' goal.
The impressive Carchedi went close again soon after, his header needed a goal line clearance from midfielder Danny Wood.
The Blades began to creep back into the game, Colin Cryan unlucky to see his downward header bounce over.
Parker almost turned the ball into his own net, but the ever improving Bradley Hughes reacted quick enough to save.
Town held out until half-time and then killed the game off early on.
After 48 minutes Town made it two. Ash Hildred's close range effort was palmed away by Rogers, only to fall into the path of Jevons who finished into the empty net.
3 minutes later the game was over. Carchedi's overhead kick stuttered into the path allowing Iain Ward to calmly finish past Rogers.
With the game already won, Town began to relax. Mark Newton's long range effort produced a fine save from Rogers but other than Kirk Wheeler's late block, little of note took place.
Sheffield United: Rogers, Wood, Armstrong, Harper, Cryan, Robertson, Sestanovich, Ross, Parkinson, Sharp, Hurst. Subs : Lindley, Marrison, Speight, Ashmore, Gyaki.