Full-time from the County Ground
Lee Gregory and Steve Morison scored twice in the opening 14 minutes and The Lions looked to be heading for another awayday win as they cruised into a 2-0 lead.
However Swindon reduced the arrears on 63 minutes with a Nicky Ajose penalty and then stunned Neil Harris' side with an equaliser in the dying seconds of injury time courtesy of Doughty's close-range header.
Harris had named an unchanged team for the second successive match with Carlos Edwards continuing at left-back in place of Joe Martin, who served the second match of a two-game suspension.
The Lions came flying out of the traps and with just two minutes on the clock a urging run from right-back Mahlon Romeo set up the first real chance of the game. Picking up the ball in his own half, Romeo picked off three players before laying the ball into the path of Jed Wallace, whose inviting cross was cleared by Nathan Thompson's diving header.
A long pass from Wallace sliced open the home defence after four minutes, but Gregory was denied as he prepared to pull the trigger by a superbly last-ditch tackle from.Raphael Rossi-Branco.
Gregory didn't have to wait too long to get his name on the score-sheet, however, and when Shane Ferguson played the resulting corner short to Wallace the latter's pinpoint delivery was turned home by Millwall's in-form striker for his 22nd goal of the season.
It could have been goal number 23 of the campaign for Gregory on 11 minutes when he was played in by Morison's wonderful slide-rule pass. Having worked his way past keeper Lawrence Vigouroux Gregory lost his bearings a little and fired wide of the target with the goal at his mercy.
Swindon skipper Nathan Thompson was booked three minutes later for a poor challenge on his namesake Ben, but thankfully the tigerish Millwall midfielder was able to continue.
A piece of quick thinking by Vigouroux prevented The Lions possibly adding a third goal with the home keeper sprinting out of his goal to head clear after another Wallace pass arrowed towards Gregory.
Swindon began to settle down following their nightmare start to the game and Brandon Ormonde-Ottewill did well to create an opening on the left flank, but undid his hard work by wildly lashing the ball yards off target.
It took a great 35th-minute block from Edwards to avert the danger after Michael Doughty's cross from the left fell into the path of Bradley Barry, but the latter's stinging shot was expertly cleared for a corner which failed to trouble a resolute visiting defence or keeper Jordan Archer, who was virtually a spectator during the first-half.
The second-half was just two minutes old when Ferguson lofted an inviting cross met by the head of Morison, who powered his effort a foot wide of the right hand post.
Byron Webster was unlucky with two stabs at the ball from a Wallace corner, the first effort blocked on the line and the second bouncing behind for a goal kick.
Swindon were handed a lifeline on 63 minutes when Edwards was harshly penalised for a foul on Barry and Ajose fired the resulting spot-kick into the top-right corner to pull one back for the hosts.
Luke Williams' side really had their tails up now as they prised and probed in search of a second goal.
Ajose sent a header over the bar from sub Anton Rogers' hanging cross before stinging the palms of Archer's hands with a rasping 75th-minute drive that the keeper gathered at the second attempt.
Webster expertly nicked the ball off the toes of Ajose as he weaved his way into the danger zone and defensive partner Mark Beevers then threw himself to clear James Brophy's deep cross as The Lions found themselves under increasing pressure.
Millwall looked to have dug in for three more precious points only for Doughty to steal in and head home Barry's deep cross to deny The Lions a victory that for so long looked to have been theirs for the taking.
Booking: N. Thompson (14mins), L. Thompson (69mins), Rossi-Branco (71mins)
Scorer: Ajose (63mins, pen), Doughty (90+4mins)
Millwall: Archer, Romeo, Edwards (Upson, 84mins), Beevers, Webster, Abdou, Thompson, Ferguson, Gregory (O'Brien, 77mins), Morison, Wallace. Subs not used: Forde, Williams, Onyedinma, Nelson, Philpot.
Bookings: Wallace (69mins), Romeo (85mins)
Scorers: Gregory (7mins), Morison (14mins)