Danny Schofield picked the perfect time to score his first goal for The Lions with a late leveller to secure a share of the spoils in a feisty contest at the County Ground.
Schofield, a 53rd-minute replacement for Dave Martin, kept his head while others around him threatened to lose theirs to cancel out Scott Cuthbert's 14th-minute opener.
In a game littered with some quite perplexing officiating at times, both teams finished with 10 men as Swindon's Jonathan Douglas (26mins) and then Millwall's Andy Frampton (66mins) were shown straight red cards for fouls on Jimmy Abdou and Jon-Paul McGovern respectively.
Millwall last tasted victory on the road 12 games ago when Jason Price's injury-time goal secured a 1-0 win at Crewe on 28th March, but they will be left kicking themselves at not coming away from this match with all three points.
Swindon were always going to provide tough opposition, with Danny Wilson's Robins coming into this game unbeaten since the opening day of the season when Gillingham rattled in five goals without reply.
The home side started brightly and there was as early scare when The Lions allowed Ben Hutchinson to slip free on the right, but he dragged his effort wide.
Hutchinson then saw a rasping angled drive parried by David Forde as The Robins pressed forward.
In a crisp opening both teams seemed intent on playing free-flowing attacking football and The Lions produced some decent moves of their own.
A teasing James Henry delivery was held by David Lucas in the home goal before Millwall came close to breaking the deadlock on 13 minutes.
Former Swindon defender Jack Smith saw his shot from a Henry cross pushed onto the woodwork by Lucas, and although Abdou got a bit of the ball, he made more contact with with the foot of the post as he tried to ram home from a yard out.
Seconds later play had swung up the other end and from their first corner of the game, McGovern picked out Cuthbert to rise high and head home the opening goal.
Back came The Lions with deliveries from Martin and Henry inches away from Alexander and Laird respectively.
On 23 minutes a long, high hanging clearance from Tony Craig saw Martin produce a sublime piece of skill to leave Kevin Amankwaah in his wake before curling over a cross that flashed across the face of goal.
Swindon had been forced to defend a period of sustained Millwall pressure when when Douglas was shown a straight red card for a raking challenge on Abdou.
Referee Wright had no hestitation in dismissing the Swindon man - and it didn't take long for Robins winger Anthony McNamee to have his name taken for a petulant foul on Henry.
The Lions kept their foot on the gas in a bid to break down a resilient Robins defensive wall with Craig's header from a Martin corner well held by Lucas, Smith's tame shot comfortably saved by the keeper and then both Marc Laird and Abdou seeing efforts testing the home defence.
But for all their possession, Jackett's men couldn't make any of their opportunities count before the break.
On came Neil Harris and then Schofield in quick succession, with Harris teeing up a gilt-edged opportunity for Steve Morison to level on 59 minutes.
Having picked up a neat ball from Barron, Chopper twisted his way into the area before picking out the unmarked Morison seven yards out. The former Stevenage striker opted for power rather than precision, and sliced the ball over with the net gaping.
No sooner had Henry hobbled off injured just past the hour-mark than Millwall found themselves reduced to 10 men.
Frampton miscontrolled a high ball on the halfway line letting McGovern in, with Frampton's subsequent lunge sending the Swindon midfielder crashing to the ground.
Out came the second red card of the game, with Harris and Amankwaah also booked by the referee following a frank exchange of views.
But spurred on by some fantastic vocal support, The Lions re-grouped and battered away relentlessly in search of that elusive equaliser.
Morsion headed Schofield's deep delivery into the side netting and a magic moment by Harris nearly conjured up a goal with quarter of an hour remaining, only to see his exquisite curler smack the right-hand post with keeper Lucas stranded.
With time ticking away it looked as if it was going to be another afternoon of 'so nearlys' for Millwall.
But when Barron picked out Morison with another pinpoint delivery, the frontman laid the ball off perfectly for Schofield, who took one touch before firing home Millwall's first League goal away from The Den since the opening day of the season.
With the bit firmly between their teeth, there only looked to be one team likely to go on and win the match, with Chris Hackett's piledriver producing the save of the match from Lucas, who pushed the ball away for a corner.
Unfortunately the officials failed to spot that, awarding a goalkick instead.
If that decision was strange, worse was to follow.
When The Lions won a corner in the dying seconds of injury-time, Hackett swung the ball over to the unmarked Craig, who was clearly shoved in the back - sending his effort over the bar instead of into the back of the net for a winning goal.
Swindon Town: Lucas, Cuthbert, Douglas, Greer, McGovern, Hutchinson (Timlin, 32mins), McNamee (Jean-Francois, 46mins) , Amankwaah, Kennedy, Ferry, Revell (Paynter, 80mins). Subs not used: Smith, Easton, Morrison, Peacock.
Bookings: McNamee (31mins), Amankwaah (66mins), Paynter (86mins)
Sending off: Douglas (26mins)
Scorer: Cuthbert (14mins)
Millwall: Forde, Smith, Barron, Laird, Craig, Frampton, Martin (Schofield, 53mins), Abdou, Alexander (Harris, 46mins), Morison, Henry (Hackett, 60mins). Subs not used: Sullivan, Dunne, Bolder, Price.
Bookings: Schofield (56mins), Harris (66mins)
Sending off: Frampton (64mins)
Scorer: Schofield (82mins)
Ref: K. Wright
Att: 7,222 (away 552)