Bayer Leverkusen’s Florian Wirtz laid on a backheel for Undav’s opener after 30 minutes in Zenica.
The Stuttgart forward then made it two when he turned in Maximilian Mittlestaedt’s cross.
Bosnia hit back with 20 minutes remaining when 38-year-old former Manchester City forward Edin Dzeko headed in from a corner for his 67th international goal.
The win moves Germany on to seven points from three games, two ahead of the Netherlands with the two heavyweights facing each other on Monday in Munich.
At the Puskas Arena in Budapest, Hungary and Dutch players, as well as spectators, observed a minute’s silence in memory of former Netherlands great Johan Neeskens who passed away this week at the age of 73.
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