Stephen Day scored a hat-trick for the Fifers at Albert Park on Saturday, with Craig Martin and Jack Cowan also netting and an own goal taking the final scoreline up to the half-dozen mark.
That win lifts Oakley up to third place in East of Scotland Football League first division conference B with 30 points from 15 games.
Hawick remain second bottom of the 15-team table with five points from 16 games, just a point above Newburgh Juniors, and the basement side have two games in hand.
The Borderers’ other 6-0 defeats this league campaign were at home to Kinnoull in July, away to Burntisland Shipyard later that month and away to Peebles Rovers in September.
They’re among 13 losses inflicted upon the Teries this season, the biggest of them being a 9-1 thumping away to Glenrothes in Fife in their opening game of this term on Saturday, July 17.
Glenrothes, currently top of conference B with 37 points from 15 games, are next up for manager Jordan Gracie’s side following a blank weekend coming up.
That game, at Albert Park on Saturday, December 4, kicks off at 2.30pm.
Peebles, currently ninth in conference B with 18 points from 14 games, also have this coming weekend off and return to action a week on Saturday on the road at seventh-placed Luncarty in Perth and Kinross.
That game at the Bleachers’ Brownlands Park home ground kicks off at 1.30pm.