Ian Hodges could have had a hat-trick in the first 15 minutes, heading over from close range and drawing a point-blank save from keeper Kieron Jimmy.
In between, Hodges gave Hampton a 12th minute lead, heading in Elliott Godfrey's cross.
Hampton keeper Matt Lovett made a great save at his near post, while Matt Elverson and Godfrey missed chances to extend the visitors' lead.
Ten minutes into the second half, Harrow drew level from the penalty spot. The Beavers went back on the attack and Dean Wells' free-kick was diverted onto the bar before Jimmy denied substitute Law-rence Yaku.
The winner came when Godfrey latched on to Harrow defender Gary Meakin's misplaced headed and slotted the ball past Jimmy.
Yaku hit the bar late on as the Beavers hung on to stay in eighth place.
Hampton & Richmond: Lovett; Harper, Ulasi (Gardner, 64), Elverson, Paris, Wells, Inns, Godfrey (Henry-Hayden, 71), Hodges (Yaku, 38), Fernandes, Matthews.
Attendance: 156.
Hampton go to lowly Slough Town on Saturday.
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