Garner took his tally for the campaign to 14 with a strike in each half as the visitors secured their first away league win of the year.
Chesterfield lost Sam Hird in only the third minute when the defender was red carded for pulling back Garner. From the resulting free-kick Paul Gallagher forced a brilliant save from Tommy Lee.
Garner headed against a post in the ninth minute but the striker put Preston ahead on the half-hour mark when he headed in a cross from former Chesterfield front man Kevin Davies.
Lee saved from Scott Laird as the visitors pressed for a second but Chesterfield had a chance of their own in the 58th minute when Byron Harrison headed a Sam Morsy cross wide from 10 yards.
Harrison shot over in the 66th minute after a cross was flicked on but Preston finally made their superiority count 11 minutes from time when Garner headed in from close range following a corner.