The Blues were shocked in the 13th minute as Mislav Orsic raced through to finish off a brutal counterattack. Pierre-Emerick Aubameyang later had the ball in the back of the net but Ben Chilwell had been caught offside when he met Mateo Kovacic's pass to tee up the debutant.
While they held plenty of possession throughout the game, Chelsea struggled to trouble the hosts and have consequentially been made to wait for their first point on the continent this term.
There was plenty of nice link-up play between the front three in the early stages, while the Blues saw plenty of possession as they had almost complete control of the ball. There were some good recoveries made when Dinamo threatened to break forward in the second period.
Despite their possession, Chelsea were guilty of playing a number of sloppy passes, and they also needed to play the ball quicker as they were unable to penetrate Dinamo Zagreb's deep and resolute defence.
Having been unable to truly test goalkeeper Dominik Livakovic, they were cut open far too easily as Orsic raced through to open the scoring. While the hosts were pushed deep, Chelsea were never able to make them truly uncomfortable.
Manager rating (out of 10)
Thomas Tuchel, 5 -- The Chelsea manager will be left furious with his players after an underwhelming performance, especially as nothing Tuchel tried could make enough of an impact to at least rescue a point. Those frustrations came out as he received a yellow card.
Player ratings (1-10; 10 = best, players introduced after 70 minutes get no rating)
DF Cesar Azpilicueta, 5 -- Did the basics on the ball but struggled when it came to finding any sort of killer pass. Also struggled to match Orsic whenever he got going.
DF Wesley Fofana, 4 -- Was unable to keep up with Orsic as he burst forward and scored the game's only goal, while the Frenchman struggled to deal with Bruno Petkovic's physicality. Made slight improvements as the match progressed and looked comfortable on the ball in forward areas.
DF Kalidou Koulibaly, 4 -- Was beaten to the header by Bruno Petkovic for the opener, and while he made a good tackle to stop Ademi he was beaten too easily at times. Booked for fouling Orsic when the Croatian beat him to the ball and had other times where he was too slow to react. His late chest to Christian Pulisic could have ended up being an assist.
MF Reece James, 5 -- Got into good positions but his passing was poor at times, as was his crossing in the first half with too many of his attempts tamely hitting Robert Ljubicic. Almost found Armando Broja at the back post after doing well to reach Jorginho's pass. Struck the post with a shot in the latter stages.
MF Mason Mount, 5 -- Moved the ball fairly well in the middle but struggled whenever it came to making things happen in the final third throughout most of the game, although he was unlucky to see an intelligent cross headed away and then an instinctive effort saved. Booked for dissent.
MF Mateo Kovacic, 6 -- Moved the ball brilliantly at times and was one of the few players who successfully broke the lines at all, although Ben Chilwell was offside when he found the wing-back with a searching pass. There was a sloppy period towards the end of the first half.
MF Ben Chilwell, 5 -- Headed away Orsic's shot well. Got forward a lot of the time but found himself being well-marshalled by Sadegh Moharrami and Stefan Ristovski. Did well to reach Kovacic's pass to give Aubameyang a chance but was caught marginally offside. Summed up Chelsea's night when his throw-in went into play and back out without touching anyone.
FW Kai Havertz, 5 -- Had encouraging flashes with some good runs and crosses that came close to finding Aubameyang, although a poor touch let him down when there was a chance to break through later in the half. Was too indecisive when there was a chance to break forward after Josip Misic lost the ball but was then unlucky to have his header blocked.
FW Pierre-Emerick Aubameyang, 4 -- Was involved in some nice link-up play in the early stages but he needed to be more ruthless in the opposition box -- his wastefulness was accentuated by Orsic's goal. There were a few times where the debutant wasn't quite on the same wavelength as his new teammates.
FW Raheem Sterling, 4 -- His first half was epitomised when he made a good run to get into the opposition box before eventually being crowded out and losing the ball. Completely wasted the opportunity to counter by making a poor pass following a Dinamo mistake and didn't do much in the second period.
Hakim Ziyech, 3 -- Replaced Azpilicueta at halftime and showed early intent with a shot from range, even if it didn't trouble Livakovic. Was largely ineffective, hitting some horrible shots and crosses, but almost found Broja with a cross into a dangerous area. Smashed an effort straight at Livakovic from close range. His night was encapsulated by him catching the ball before it had gone out of play.
Jorginho, 5 -- Replaced Kovacic in the 59th minute and tried to move the ball and make things happen, but couldn't manage to find a way through the Dinamo defence.
Armando Broja, 5 -- Replaced Aubameyang in the 59th minute and flashed a ball towards the front post moments after coming on as he tried to inject some extra energy into their play.
Marc Cucurella, N/R -- Replaced Chilwell in the 71st minute and was unable to make many notable attacking moves, while he was beaten to the ball a few times while trying to defend.
Christian Pulisic, N/R -- Replaced Sterling in the 75th minute and tried to get into dangerous areas but couldn't quite make them count. His header in the final moments went nowhere near finding the goal.