The home side took a grip from the outset and were never in any danger and after some neat passing football, took the lead on 15 minutes when a Michael Warner cross in from the right was flicked into the back of the net by controversial front man Anthony Elding.
With their noses in front Stevenage tormented the visitors, Simon Weatherstone and George Boyd both coming close, before they all but sealed the points on 37 minutes.
The home side constructed a stunning move which contained no less than 12 passes, the ball moved from defence to attack before Darryn Stamp fired home into the bottom right-hand corner of the net.
It was a strike worthy of a goal of the season and left the visitors with no way back into the contest.
The second half followed a similar pattern and although Altrincham did come close with a strike hitting the foot of Alan Julian's post it was otherwise all one-way traffic with Stevenage grabbing the third on 72 minutes when Dino Maamria fired a penalty into the bottom left-hand corner after Val Owen had handled in the box.
Further chances fell to the home side as they peppered hapless Altrincham to the last.
It was ironic that their best chance came two minutes into added time when a foul by keeper Stuart Coburn on Boro sub Jon Nurse gave the home side a penalty which Elding scored, only for Coburn to save it when it was retaken due to an infringement.