Forest opened the scoring in the 18th minute when Mackie received a ball from Jamaal Lascelles before curling a superb left-footed effort into the top corner from the edge of the area.
Simon Cox had a great chance to double Forest's advantage but shot wide from close range before Preston upped the ante in the second half in search of an equaliser.
Forest keeper Dorus de Vries had plenty to do as Simon Grayson's charges pressed and they were desperately unlucky when substitute Joe Garner's effort was blocked onto the post by a sliding Lacselles.
As Preston went after the visitors, Henderson ensured the victory for Forest when firing a half-volley home in injury-time to send the Premier League promotion-chasers through to the next phase.
2013/14 FA Cup fourth round replay
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