The hosts went in front through Luke Cundle but a red card for Zak Sturge changed the contest dramatically, and Michael O’Neill’s side produced a late comeback that moved them three points clear of the relegation zone.
It was the perfect response from Rovers after a disappointing defeat at relegation rivals Oxford in midweek.
It took 23 minutes for the first decent effort from either side as Taylor Gardner-Hickman’s free-kick needed tipping over by Millwall goalkeeper Anthony Patterson.
This led to Rovers being the first to settle and they missed a great chance to go ahead when Eiran Cashin met Todd Cantwell’s cross with a header that drifted wide.
Millwall failed to have a shot in the first half, but they were nearly ahead four minutes after the restart when Femi Azeez’s cross was cleared as far as Barry Bannan, whose effort was pushed behind by Balazs Toth.
It did not take the Lions quite as long to have their second attempt as, a minute later, Camel Neghli’s lovely ball into the box was headed over by captain Jake Cooper.
The hosts led after 54 minutes when Azeez’s cross was met by a superb overhead kick from half-time sub Cundle that nestled in the bottom corner.
A chance to double the lead on the counter soon came along as Josh Coburn’s pass sent Neghli galloping towards the area, but his shot across goal went narrowly wide.
Then came a big twist as Millwall went down to 10 men in the 59th minute when Sturge was shown a straight red for pulling down Yuki Ohashi as he was trying to run through on goal.
Thrown a lifeline, Rovers went on the attack with Ryan Alebiosu having a shot saved by Patterson, but the Lions were a threat on the break as Azeez fired narrowly over from a tight angle.
O’Neill’s men had their equaliser in the 80th minute when Ohashi’s pass put Alebiosu in behind and his ball across the six-yard box gave Jorgensen the simplest of tap-ins.
And a dramatic late turnaround was completed five minutes later when Ryoya Morishita’s pass found Jorgensen in space and the Dane swept his shot into the bottom corner to give Rovers a priceless victory.