The 21-year-old, signed from Scunthorpe in the summer, struck in the first half with Luton Shelton grabbing two and midfielder Lee Hendrie scoring his first for the side since his move from Aston Villa.
United boss Bryan Robson took no chances, fielding a strong team against the Lancashire club who are enjoying their first season of league football.
Morecambe, who have had a steady start in League Two, had already disposed of Championship sides Preston and Wolves in the earlier rounds.
Shelton, signed last season from Swedish side Helsingborgs for £1.8million, set up United's opener on 18 minutes with a mixture of pace and skill.
The lanky striker weaved past three defenders before slipping the ball inside to Sharp who finished with a left-foot strike into the roof of the net from 10 yards.
United escaped on the half hour when a poor clearance fell to the feet of Craig Stanley .
The midfielder's fierce strike was tipped around the left-hand post by Paddy Kenny in spectacular fashion before United swept further ahead three minutes later.
Full-back Derek Geary, who was back in the side after a three match suspension, threaded the ball to Sharp who charged into the area before hammering his left-foot drive past Joe Lewis from 16 yards.
Michael Twiss almost found a way through and Stanley had a curling cross-cum-shot snatched by the diving Kenny before Shelton killed off Morecambe on 52 minutes.
He ran on to Stephen Quinn's pass to round Lewis and slot the ball into an empty net.
Hendrie added the fourth in the 67th minute with Shelton grabbing his second of the night four minutes later.