The result at Signal Iduna Park means leaders Dortmund need a win at Zenit St Petersburg next Tuesday to be sure of progressing as Group F winners.
Lazio, who are second and a point behind the Germans, will also go through if they draw at home to Club Brugge the same night.
Immobile, who failed to make his mark in the Bundesliga after an unhappy 2014/15 season at Dortmund, converted a 67th-minute penalty to cancel out Raphael Guerreiro’s goal just before half-time.
We move ✅ https://t.co/sC1WB3bWct
— Borussia Dortmund (@BlackYellow) 1606946244000
The draw could have come at a cost as Dortmund defender Mats Hummels had to be helped off after Immobile trod on his ankle in the dying stages.
Even though their star striker Erling Braut Haaland dropped out just before kick-off, Dortmund did enough to reach the knockout stages.
Haaland, the top scorer in the Champions League this season with six goals in four games, was sidelined by a leg injury.
Dortmund have not said how long he will be out for.
The points are shared, but we are through! ✔️ https://t.co/3AxxFPA3xt
— Borussia Dortmund (@BlackYellow) 1606945918000
In his absence, captain Marco Reus moved further up front and Dortmund deservedly went ahead just before the break.
Lazio’s veteran goalkeeper Pepe Reina, 38, played out a weak clearance which was snapped up by Dortmund midfielder Thomas Delaney.
The Dane moved the ball quickly to Guerreiro, who passed off to teenager Giovanni Reyna and sprinted into the area onto Thorgan Hazard’s final pass, which he fired past Reina a minute before half-time.
However, Immobile was a constant menace for Dortmund goalkeeper Roman Burki, who palmed away a fierce shot with an hour gone.
Guerreiro made way for Nico Schulz as Dortmund head coach Lucien Favre strengthed his defence, but the substitution soon had repercussions.
Schulz had only been on three minutes when he lunged into a clearance in the area and made contact with Lazio midfielder Sergej Milinkovic-Savic.
Lazio were awarded a penalty which Immobile duly converted.
Lazio finished the stronger and only a superb diving save by Burki just before the final whistle pushed Immobile’s well-struck effort around the post.
Immobile collided with Hummels late on and the 2014 World Cup winner needed assistance in leaving the pitch.