Referee Paul Danson proved to be the crucial figure in a match of many incidents. Danson sent Luton manager Mike Newell from the dugout in the 28th minute, showed red cards to two players and booked seven more.
Leicester referee Danson also ordered a Luton penalty to be retaken as Swindon stormed back to equalise in the last minute of normal time.
Newell was sent to the stands for dissent for the second time this season while Swindon's Stefani Miglioranzi and Luton's former Swindon full-back Sol Davis were sent packing in separate incidents.
All this over shadowed an exciting match in which Swindon took the lead in the eighth minute when James Milner, completing a loan spell from Leeds glanced home a cross from the left by Sammy Igoe.
After Miglioranzi and Davis had been sent off, Luton equalised in the 62nd minute when Jerel Ifil brought down Gary McSheffrey and although Rhys Evans saved the first spot kick from McSheffrey the busy Danson ordered a re-take and this time the same player made no mistake.
Swindon were still fuming when Luton striker Adrian Forbes cut in from the right to beat Evans with a low right-foot shot from 12 yards.
Swindon, unbeaten since defeat on the opening day, stormed back in a desperate bid to preserve their nine-match unblemished record and only a goalline clearance from Russell Perrett denied Milner a second in the 75th minute.
Swindon got their equaliser in the last minute of normal time when Luton failed to clear a free kick taken on the edge of the area by Andrew Gurney and sub Brian Howard lashed in the rebound with a left-foot shot from 15 yards, only to be booked for celebrating at the conclusion of an extraordinary contest.