Late goals from Pierre-Emerick Aubameyang and the Italy international salvaged a draw after Daniel Didavi had put the visitors 2-0 ahead
The visitors announced the sacking of sporting director Fredi Bobic shortly before kick-off after a dismal start to the season saw them sitting bottom with one point from four matches.
However, Daniel Didavi's strike three minutes into the second half gave Stuttgart an unlikely lead, before the midfielder doubled his tally 20 minutes later.
Pierre-Emerick Aubameyang halved the deficit in the 73rd minute, but the home side looked destined for a second consecutive top-flight defeat after losing 2-0 at Mainz last time out.
That was until Immobile popped up at the far post to hook the ball home from a Marcel Schmelzer free kick four minutes from time.
Lukasz Piszczek came agonisingly close to snatching all three points for Dortmund in injury time, only for Antonio Rudiger to produce a superb goalline clearance after the Pole had fired beyond Sven Ulreich.
The draw leaves Dortmund in mid-table with seven points from five matches, while Stuttgart climb off the foot of the table on goals scored.
Captain Mats Hummels was fit enough to take a seat on the Dortmund bench - a rare positive piece of team news for the depleted hosts who had the likes of Marco Reus (ankle), Henrikh Mkhitaryan (foot), Nuri Sahin (knee), Jakub Blaszczykowski, Oliver Kirch and Ji Dong-won (all muscle) all sidelined.
But it was the home side who started stronger, with Shinji Kagawa sending a tame effort into the arms of Ulreich from the edge of the penalty area, before Milos Jojic offered the Stuttgart goalkeeper some more catching practice from a similar distance.
Stuttgart took time to settle, but made a rare attacking foray in the 10th minute when Christian Gentner scuffed an effort wide of the target, before Timo Werner was flagged for offside after being sent through one-on-one with Roman Weidenfeller.
For all their possession early on, Dortmund were struggling to carve out any clear-cut opportunities, and Weidenfeller had to be alert at the other end in the 23rd minute - diving low to his right to deny Werner from a tight angle.
Dortmund finally started to look dangerous just after the half-hour mark when Kagawa breached the Stuttgart defence, only to lift his effort onto the top of the crossbar, and Jojic fizzed a venomous strike just over.
However, Stuttgart silenced the home fans in the third minute of the second half - Didavi side-footing home after Gentner had rolled the ball into the centre of the penalty area.
The goal initially sparked Dortmund into action, but a lack of cutting edge in the final third was proving costly, while Stuttgart - sitting deeper after going ahead - continued to look dangerous on the break.
And Armin Veh's side doubled their lead in the 68th minute.
Schmelzer failed to clear his lines from a long pass, and Werner's simple pass teed up Didavi for an equally straightforward finish from close-range.
Kagawa headed just wide moments later, before Aubameyang took the ball around Ulreich and tucked home from a tight angle.
Stuttgart looked like clinging on for a deserved and unexpected victory, but Immobile - anonymous for the most part - found himself in the right place at the right time to draw Dortmund level before Rudiger's heroics denied Klopp's side all three points at the death.