Manager Peter Duffield fielded the same front three that played in the second half on Saturday, as Mark Ward, Evan Garnett and Kieran Wells were tasked with leading the line for the Nailers.
After a strong comeback at the weekend, Belper were hoping to follow on from their second half showing with character and quality.
However, struggles in front of goal proved all too much for the away side, as the Ravens rolled onto the next round with a glamorous draw against Lowestoft Town.
The first half belonged to the Nailers overall, with the main chances coming for Kieran Wells, but to no avail.
The Ravens had their best opportunity on the stroke of half time as Ash Way struck a central free kick from 20 yards, which was tipped over the bar well by Scott Low.
Kieran Wells had three great opportunities go amiss in the second half, as the Nailers continued to search for their first win of the season.
The best of the bunch coming on the 47th minute after Mark Ward found space inside the area, before squaring the ball to Wells who could only shoot straight at the 'keeper.
Evan Garnett then had a good chance on the 58th minute to give his side the lead.
This time an Ian Ross cross from the left hand side was swung towards the far post where Garnett opted to side foot the ball with little conviction, dropping wide of the near post
The first goal came on the 59th minute when Jake Woolley pulled a cross back from the by-line on the left hand side, after getting in behind Aaron Pride, to find the unmarked Stuart McNaught at the far post, who side footed the ball into the bottom corner with consummate ease.
Mark Ward then had a good opportunity to equalise a minute later from a free kick on the edge of the box, right of centre, only for the ball to rise a yard over the bar with the goalkeepercovering his lines.
The game was then put to bed with 5 minutes left to play as Woolley found Jed Davies on the left who weaved his way through the challenges to slot the ball past the goalkeeper in fine style.
There was however a late red card for Coalville Town as 85th minute substitute Matt Brown was sent to the stands just moments after his arrival, following an elbow in the face of Aaron Pride after the two players leaped to head the ball.
Coalville Town: Sean Bowles, Jack Farmer, Liam Key, Sam Saunders, Jamie McAteer, Alex Dean (Ash Way 11), Lee Miveld, Danny Edwards, Jake Woolley (Matt Brown 85), Stuart McNaught, Jed Davies (Sam Moore 90). Subs: Cameron Stuart, Olly Brown-Mill.
Belper Town: Scott Low, Aaron Pride, Billy Bennett, Ian Ross, Regan Edridge, Matt Varley, Simon Harrison (Colin Marrison 75), Steve Warne, Mark Ward (Jon Froggatt 74), Evan Garnett (Rob Stevenson 63), Kieran Wells. Subs: Mark Dudley, Lee Thompson, James Martin.
Referee: Andrew Fox (Rugby)
Attendance: 182