The Italian striker arrived at Signal Iduna Park during the close-season from Torino and was a second-half substitute in Dortmund's 1-1 draw on Tuesday.
Dortmund recovered from going behind to a first-half penalty from Nicolas Feldhahn to earn a draw thanks to Henrikh Mkhitaryan's strike just after the hour.
Immobile had a chance to win the match late on, only for Daniel Heuer Fernandes to deny him with a good save.
Like in their opening pre-season game against Hessen Kassel, which ended in a 4-1 win, Dortmund failed to convert some decent chances, with Pierre-Emerick Aubameyang and Jonas Hofmann guilty of spurning opportunities.
Jurgen Klopp's men were punished for their profligacy just after the half hour as Osnabruck took the lead from the penalty spot.
Having being held back by Ji Dong-won inside the penalty area, midfielder Feldhahn opened the scoring with a well-taken spot-kick.
Aubameyang had a chance to level in the closing minutes of the first half, but his effort was well blocked.
Klopp changed his entire team at half-time, including introducing debutant Immobile.
The Italy international was immediately involved in the action and attempted an audacious effort from 35 yards in the 50th minute that sailed just wide.
Immobile's presence was causing the Osnabruck defenders plenty of problems, although it was fellow substitute Mkhitaryan who levelled.
With 65 minutes played, the Armenia international embarked on a mazy solo run before finding the net.
Last season's Bundesliga runners-up began to exert even more pressure, but Immobile's lack of match sharpness showed as attacking moves broke down around him.
Immobile's first real opening in a Dortmund shirt came three minutes from time as he latched onto to a pass inside the penalty area, but Fernandes made a good save to earn Osnabruck a draw.
