Things went from bad to worse for Leeds, who quickly fell 4-1 behind before Dan Ross reduced the arrears with a neatly taken volley.
The home side pushed forward in search of a third and felt that they should have had a penalty late in the game.
But with the Leeds players still protesting to the referee, New Unicorn launched a lightning quick counter attack to grab a fifth and seal the points.
The defeat leaves Maccabi nine points off league leaders Waggon Athletic, although they do have two games in hand following a number of postponements during the recent cold snap.