A resilient second half display enabled Hillians to claim victory over hosts Fisher and stretch their unbeaten run to six games in all competitions.
Manager Gary Croydon said: "We created a large amount of chances and should have won by a greater margin. Nevertheless I was happy with the three points."
Hill fell behind in the 33rd minute to a spectacular Richard Brady strike.
Eight minutes later Fisher goalkeeper Michael Holder was dismissed for handling outside the area and outfield substitute Steve Taylor was forced to deputise.
Hill found themselves ahead six minutes after the break. Sub Matt Simpson's cross was bundled home by Nicky Sullivan from close range then Steve Harper rounded Taylor to score.
Harper sealed victory with 20 minutes left. Fisher's agony was complete when Michael Smith was sent off for two bookable offences.
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