Preston could consider themselves unfortunate to be a goal down at the interval, but they made a slow start to the second half and fell further behind when Louis Carey headed home a free-kick from Paul Hartley.
Ferguson's men rarely threatened thereafter and they conceded a late fourth when Evander Sno drilled past Andy Lonergan from the edge of the area.
Ross Wallace grabbed an injury-time consolation with a wonderful curling free-kick, but it was too little, too late for the visitors.
City boss Gary Johnson handed a recall to Ivan Sproule and Lewin Nyatanga, while Marvin Elliott was among the substitutes after injuring his back in the midweek FA Cup draw against Cardiff.
Ferguson named the same side that defeated Colchester 7-0 in the FA Cup under the caretaker stewardship of Rob Kelly.
The new North End boss saw his reign get off to a terrible start as City took the lead inside two minutes.
Hartley delivered a deep free-kick from the left and Haynes escaped his marker to head home from close range.
There were further chances at either end before City doubled their advantage from another set-piece in the 12th minute.
McAllister played the ball to Hartley, who in turn fed Nicky Maynard. The striker's effort was saved by Lonergan but Fontaine was on hand to convert the rebound.
City goalkeeper Dean Gerken made a useful stop to deny Darren Carter and Wallace drilled a shot narrowly wide as Preston looked to respond.
The Lilywhites deservedly pulled a goal back in the 27th minute, Brown heading home from eight yards after excellent work from Chris Sedgwick on the right.
With City on the rack, Neill Collins and Eddie Nolan both missed the target with presentable opportunities and Parkin saw an effort ruled out for an apparent foul on his marker.
Carey then headed wide for the Robins from another Hartley set-piece, before the impressive Sedgwick threatened again with a shot across goal that Gerken did well to parry clear.
Gerken was soon forced into further action to keep out Brown's header, while Maynard tested Lonergan with a similar effort as a frantic opening period drew to a close.
The home side started the second half brightly and McAllister - playing in an advanced position on the left of midfield - should have done better when failing to control the ball following Haynes' lay-off.
Sproule was twice denied by Lonergan before City were rewarded for their pressure with a third goal in the 58th minute.
Hartley was once again the creator, swinging over another delightful free-kick that Carey rose to head home at the far post.
The goal seemed to knock the stuffing out of Preston and they struggled to reproduce the free-flowing football that had brought them so many chances in the first half.
Sno drove home City's fourth in the 90th minute following a neat lay-off from substitute David Clarkson, before Wallace curled home a consolation in the second minute of injury-time.