The Italian, criticised for a lack of Bundesliga goals this season, pounced on a cross-field pass from Dynamo’s Michael Hefele to snatch the lead five minutes after the break on a bumpy pitch that resembled a ploughed field in parts.
Dortmund, last season’s finalists, struggled to play the flowing game that has won their last four league matches and Mats Hummels almost gifted Dynamo an equaliser when his backpass bounced awkwardly and was intercepted before keeper Mitch Langerak cleared.
“You cannot expect to play good football on a pitch like that,” Dortmund coach Juergen Klopp told reporters. “This pitch is quite something and we had to play very simple football on it.”
Dortmund’s substitute striker Adrian Ramos almost got a second but his shot squeezed past a defender and hit the near post before rolling along the line and being cleared.
However, Immobile, who suffered a facial injury in the first half from Hefele’s elbow, scored again when he slotted in from a Jakub Blaszczykowski cutback in the box near the final whistle.
Dortmund winger Marco Reus, who missed much of 2014 with a string of ankle injuries, limped off midway through the first half, though his injury may not be too serious.
“I was told it may just be a knock on the leg. But I don’t know if he will be fit for the league at the weekend,” Klopp said.
Earlier, Bayer Leverkusen’s Hakan Calhanoglu rescued his side from embarrassment with a sensational free kick to steer them to a 2-0 extra-time win over second tier Kaiserslautern.
The Turkey international fired a shot around the wall from 25 metres past keeper Marius Mueller towards the end of the first half of extra-time to break the visitors’ resistance.
Stefan Kiessling added a second goal 10 minutes later after Leverkusen struggled for most of the game.
Fellow Bundesliga club Hoffenheim had a much easier task against second division Aalen with Eugen Polanski and Germany international Kevin Volland on the scoresheet.
In the all-Bundesliga clash, Freiburg got two goals in two minutes early in the first half to win 2-1 at home Cologne, who had opened the scoring when Anthony Ujah put through his own net before they netted a late consolation.
Holders Bayern Munich are in action on Wednesday against Eintracht Braunschweig.
(Reporting by Karolos Grohmann; editing by Ken Ferris)