The Town captain rescued his side from a third straight defeat, unprecedented for Paul Sturrock in his managerial career.
Leyton Orient ought to have won more than a point. Adam Boyd's 85th minute goal looked to have sealed it, but it was not to be.
Swindon, shot-shy throughout, launched one final raid forward when Orient stupidly gave away possession in midfield.
Lee Peacock headed down a cross from substitute Michael Pook and Aljofree appeared to miscue his shot past goalkeeper Stuart Nelson into the bottom corner.
Orient were kicking themselves for not strengthening their promotion claims as they had sufficient of the ball and more than enough chances to have won it.
When Boyd picked up the pieces from a late corner to put the East Londoners in front, it looked as though the visitors' general polish would shine though.
But, though their counter-attacking style was neat and effective, their finishing was often wasteful.
The impressive Wayne Gray and Adam Chambers, a constant threat, wasted several good opportunities before Boyd put Orient ahead.
Swindon, who had lost their last two matches and had slipped into mid-table, were sadly lacking as an attacking force until the closing stages.
They mustered only one tame effort during the first half and, apart from one header by Peacock later on, seldom caused Orient any real threat.
Sofiane Zaaboub caught the eye with some lively raids down the left flank for Town, but strike pair Simon Cox and Billy Paynter were generally starved of possession as the Robins failed to get the ball into dangerous areas.