The visitors came and set out their stall superbly. Although Wycombe created the best chances, the non-league side defended in a well-organised fashion.
Chris Woodhall and then Ashley Warner tested Wycombe keeper Frank Talia as the Ravens grew in confidence.
Nathan Tyson missed two great chances when in the clear, one from three yards out from a Gus Uhlenbeek cross on 41 minutes.
For Coalville, goalkeeper Sean Bowles and captain Dave Tonge were both outstanding.
In the second half Coalville kept going. With 20 minutes to go the Wycombe fitness began to tell as the visitors legs started to look heavy.
Tyson saw another crisp effort well saved by Bowles low down to his right on 65 minutes.
Wycombe finally scored on 70 minutes when a Gary Silk free-kick on the left was headed in by central defender Roger Johnson.
Coalville never gave it up for a moment and although they did not create a clear-cut chance after the home team had scored, they stuck to the task to the end.