Thomas Tuchel handed new signing Pierre Emerick Aubameyang his debut from the start, while Kepa Arrizabalaga replaced Edouard Mendy in goal.
Chelsea started on a dominant note, but Dinamo Zagreb took the lead against the run of play when Mislav Orsic raced ahead of Wesley Fofana to finish past Kepa Arrizabalaga in the 13th minute.
Chelsea continued to dominate possession, but the hosts were compact, denying them any space to cause havoc.
The first half ended 1-0 in favour of Dinamo Zagreb.
Thomas Tuchel brought in Hakim Ziyech after the restart in a bid to salvage something out of the game, but the Moroccan winger was largely ineffective in the encounter.
Armando Broja replaced Pierre Emerick Aubameyang, while Christian Pulisic replaced Raheem Sterling but the changes had no effect on the game as Dinamo Zagreb held on to earn a historic win.
Chelsea have now lost three consecutive away games for the first time under Thomas Tuchel following losses against Leeds United and Southampton.
The Blues will be back in Premier League action against Fulham on Saturday.
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