Nick Linfoot opened the scoring in the second minute to ease the visitors’ concerns.
Harry Ellis doubled the score-line in the 20th minute from a pass by a rampant Paul Kellett which invigorated the Tangerines in the closing minutes.
Matt Dickenson’s sharp shot found the net from a Paul Wright intricate pass and, in the 32nd minute, confusion in the home defence let in Sam Lynn to round the ’keeper.
Harrogate narrowed the advantage with a penalty corner just before half-time.
Acomb started the second half well and secured their four-goal advantage when Lynn deflected home a penalty corner.
After spurning a string of chances, Acomb yielded two late goals, one following a rash tackle by ’keeper Craig Brown.