Roger Johnson scored the only goal as managerless Wycombe went through.
Wycombe created chances galore in the first 10 minutes but Sean Bowles pushed over Russell Martin's strike and Nathan Tyson blasted over from six yards.
The Ravens then pushed forward on the counter-attack and Frank Talia saved well from Lee McGlinchey before Ashley Warner fired into the side netting.
Tyson headed wide from close in and had a low drive saved before Johnson headed in Tony Craig's free-kick to win it.
Wycombe: Talia, Uhlenbeek, Johnson, Williamson, Craig, Silk,
Martin, Ryan, Senda (Bloomfield 45), Tyson, Stonebridge.
Subs Not Used: Nethercott, Williams, Anya, Ahmed.
Goals: Johnson 71.
Coalville Town: Bowles, Garner, Dave Tonge, Wilkes,
Brown (Peake 78), Stevens, Woodhall (Russell 73),
Pollard (Chapman 84), Geary, Warner, McGlinchey. Subs Not Used: Fletcher, Marriott.
Booked: Brown, Dave Tonge.
Ref: M Russell (Hertfordshire).