Despite having a head-to-head record that read one apiece, Cilic was the heavy favourite but world number 56 Dodig completed the win in this all-Croat contest in 78 minutes.
The 28-year-old converted four of his eight break points to reach his third quarter-final of the season, and continues a fine run that saw him beat two-time tournament winner Nikolay Davydenko in straight sets in the first round.
In Estoril, Portugal, top seed David Ferrer of Spain beat Edouard Roger-Vasselin of France 6-4 4-6 6-3.
ATP Munich results
5-Alexandr Dolgopolov (Ukraine) beat Dmitry Tursunov (Russia) 7-6(2) 7-6(3)
4-Philipp Kohlschreiber (Germany) beat Evgeny Korolev (Russia) 6-2 6-4
Viktor Troicki (Serbia) beat Radek Stepanek (Czech Republic) 6-4 6-4
Ivan Dodig (Croatia) beat 2-Marin Cilic (Croatia) 6-4 6-2
ATP Estoril results
Pablo Carreno (Spain) beat David Goffin (Belgium) 1-6 6-2 6-2
4-Fabio Fognini (Italy) beat Paolo Lorenzi (Italy) 7-6(5) 5-7 6-4
1-David Ferrer (Spain) beat Edouard Roger-Vasselin (France) 6-4 4-6 6-3
Victor Hanescu (Romania) beat 6-Benoit Paire (France) 7-6(2) 6-4
WTA Estoril results
Ayumi Morita (Japan) beat Urszula Radwanska (Poland) 6-2 6-3
Monica Puig (Puerto Rico) beat Francesca Schiavone (Italy) 6-3 6-2
3-Anastasia Pavlyuchenkova (Russia) beat Estrella Cabeza Candela (Spain) 6-3 7-6(4)
7-Elena Vesnina (Russia) beat Monica Niculescu (Romania) 6-4 6-4
Svetlana Kuznetsova (Russia) beat Galina Voskoboeva (Kazakhstan) 6-4 6-4
4-Carla Suarez Navarro (Spain) beat Yanina Wickmayer (Belgium) 6-4 6-3
Romina Oprandi (Switzerland) beat Peng Shuai (China) 6-1 6-3
Kaia Kanepi (Estonia) beat 5-Sorana Cirstea (Romania) 6-1 6-2