Goals either side of half-time by Dean Cox and Chris Dagnall gave Orient a 2-0 cushion before Anton Rodgers replied for Swindon and Andy Williams levelled the scores with a late penalty.
Orient had the opportunity to win the match long before Swindon’s comeback – Lloyd James having a 20th-minute penalty saved after a bizarre situation which saw Tyrell Belford, Swindon’s 20-year-old goalkeeper, automatically red-carded for a foul on Dagnall.
Belford’s elder brother Cameron came off the substitutes bench and flung himself to his left to save Lloyd James’ spot-kick.
O’s did take the lead when Cox robbed Raphael Branco to score – an interval lead which Dagnall doubled two minutes after the break.
Swindon pulled goal back through an Anton Rodgers volley and, in a breathtaking finale, equalised through Williams from the penalty spot.