Immobile, who joined from Torino last month, found the net against the fourth-tier side as Dortmund's greater quality told in a one-sided affair on Sunday.
Pierre-Emerick Aubameyang netted a double, while Neven Subotic and Henrikh Mkhitaryan were also on target before Cebio Soukou grabbed a consolation for the hosts at the Stadion Essen, with all six goals coming in the first half.
However, there is likely to be some concern over the fitness of Dortmund's Italian striker after he limped off following a collision with Essen goalkeeper Niclas Heimann.
Heimann was at fault for Dortmund's opener as he was dispossessed by Aubameyang in the eighth minute, the Gabon international gaining reward for his awareness.
Immobile then fed the former Saint-Etienne man for his second two minutes later, before Subotic bundled home from close range.
The rout continued as Mkhitaryan headed home from Marcel Schmelzer's left-wing cross in the 25th minute.
New boy Immobile made it five with his maiden strike for Jurgen Klopp's men, converting after good work from Aubameyang and Mkhitaryan.
Midfielder Soukou capitalised on another goalkeeping error, this time from Hendrik Bonmann, to reduce Essen's arrears.
Immobile then came together with Heimann when chasing a loose ball just before the break, and was withdrawn during the interval as part of a flurry of changes.
The flow of the game was understandably disrupted in the second half due to the substitutions, with Dortmund taking their foot off the gas as they eased to an emphatic success.
