Kidderminster, beaten 1-0 at Exeter in August briefly threatened revenge when Simon Heslop's first goal for the club gave them the lead early in the second half.
But City hit back strongly in the final half-hour and were good value for their success.
Chris Todd got them back in the hunt with a close-range leveller just before the hour mark, and Scully took advantage of a defensive slip to hit the winner in the closing stages.
Kidderminster produced a spirited display to match their high-flying visitors for long periods. But they were not sharp enough in front of goal and, in truth, were thankful to young keeper Daniel Lewis who pulled off three excellent saves in the second half to deny City.
The hosts just about shaded the first half and former City striker Gareth Sheldon came close to putting them ahead when he saw his rasping drive turned round the post by Paul Jones at full stretch just before the break.
Four minutes after the break Heslop collected a Taiwo Atieno's flick and drove the ball home from the edge of the box.
It was the hard-working 18-year-old midfielder's first goal of his loan spell from Barnsley.
Lewis had already moved smartly to keep out a vicious deflected cross from Billy Jones, and then dug out another top-class stop from Andy Taylor's free-kick.
But Exeter's long-throw tactic through Jon Challinor, which had caused the home defence huge problems throughout the afternoon, finally paid dividends in the 59th minute when Todd stole in to head home from close range.
Twelve minutes from time a sharp counter-attack from City saw home midfielder Terry Fleming caught out as he tried to cover the backline, and Scully repaid him by blasting in a fierce volley from 20 yards.