Germany took an 11th-minute lead when Guy Demel brought down Stefan Kiessling and Podolski sent the keeper the wrong way from the penalty spot.
The Ivorians equalised in bizarre fashion. Half-time substitute keeper Manuel Neuer attempted to clear a back pass but the ball bounced off Emmanuel Eboue and dribbled into the net.
Seydou Doumbia put the visitors in front after 85 minutes with a blistering drive before Podolski's late strike.
Berbatov becomes Bulgaria's top goal-scorer
Dimitar Berbatov became Bulgaria's all-time leading scorer with 48 goals after netting twice in a 4-1 win against Malta in a friendly on Wednesday.
The 28-year-old Bulgarian captain and Manchester United striker scored from close range in the 75th minute to equal former midfielder Hristo Bonev's tally of 47 goals.
Berbatov added his second seven minutes later to break the record in his 74th international.
Valeri Bojinov and Blagoy Georgiev were also on target for Bulgaria while Michael Mifsud scored Malta's consolation seconds after the interval with an easy finish.
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