Campbell, who came off the bench to provide the decisive strike in a 2-1 win at Newcastle United in the last round, repeated the trick at the Reebok Stadium, scoring the only goal of the game to send his side through to the fifth round for the first time in four years.
The former Sunderland man tucked the ball home from a tight angle in the 50th minute after Andy Lonergan failed to deal with a cross from Craig Noone, another substitute.
Bolton were unable to find a leveller as they attempted to put last week's embarrassing 7-1 defeat at Reading behind them.
Neither goalkeeper was stretched in an uneventful opening half, Lonergan comfortably tipping Cornelius' deflected shot over the crossbar in the seventh minute.
In first-half stoppage time, Bolton's Lee Chung-Yong sent a left-footed volley a yard wide after a loose ball had dropped to him inside the area.
Alex Baptiste got his head to Noone's cross from the right and the ball was spilled by Lonergan to the feet of Campbell, who swivelled and swept home into an empty net from close to the byline.
Campbell wasted a chance to double his side's advantage within six minutes, heading over from four yards after Lonergan once again struggled to deal with a ball into the box.
Marshall then had to scramble to his right as Davies' cross was deflected towards goal in the 62nd minute.
Five minutes later Marshall was called into action again, flying to his right as Ben Turner deflected Baptiste's cross with his outstretched leg.
Freedman's side have just one win from their last six matches in all competitions.
