Mislav Orsic has scored 18 goals in European competitions for Dinamo Zagreb
The Croatian champions have a woeful record in this competition - winning just five of 43 games before this meeting - but they stubbornly held on after taking a first-half lead.
The dangerous Mislav Orsic netted the 13th-minute winner, running through from the halfway line and beautifully dinking a finish past the advancing Kepa Arrizabalaga.
Dinamo came agonisingly close to a second but Stefan Ristovski's thunderous, long-range effort was superbly tipped on to the bar by Arrizabalaga.
Deadline-day signing Pierre-Emerick Aubameyang was handed his Chelsea debut and, although the ex-Arsenal skipper had a goal ruled out for offside, he largely looked off the pace.
Armando Broja replaced Aubameyang just before the hour mark, but the Albanian had little impact in an overall disjointed performance from Thomas Tuchel's men.
Chelsea launched a late onslaught on Dinamo's goal and the hosts were relieved to see Reece James' low shot rattle the foot of the post with five minutes remaining.
In Group E's other game, Serie A champions AC Milan drew 1-1 against Austrian champions FC Salzburg.
In the first transfer window under their new owners, Chelsea were Europe's highest spending club with an outlay close to £300m on new signings this summer.
The Blues, though, look an incoherent outfit and although Tuchel - who took charge of the side for the 100th time against Dinamo - is not yet under pressure, the German will quickly need to work out his side's problems with hands-on new owner Todd Boehly watching closely.
A solid defensive platform was the bedrock of Tuchel's success in his first few months at the club, when he led them to their second Champions League title with victory over Manchester City.
But in seven games in all competitions this term, the Londoners have already lost three times and kept just one clean sheet, which came on the opening day of the Premier League campaign against Everton.
Former Napoli centre-back Kalidou Koulibaly is an experienced Champions League player, but defensive team-mate Wesley Fofana was making his first appearance in the competition.
And the lack of understanding between the pair - who cost more than £100m between them - in the early days of their partnership was apparent for the goal when they both went for a high ball, yet neither got to it.
It allowed Bruno Petkovic to flick the ball on for Orsic, who held off Fofana before advancing on goal and converting with the coolest of finishes.
Arrizabalaga, who started instead of out-of-form number one Edouard Mendy, did not have much to do, but denied Ristovski with a stunning save.
At the other end of the pitch, Aubameyang was given a first start since signing from Barcelona and the 33-year-old striker played in a face mask, having been involved in a violent robbery at his home which left him with a broken jaw.
The signs were good when he ran through early on, but failed to pick out a team-mate with his cutback and struggled to make an impact thereafter.
Chelsea's general showing was one of slow build-up play which did not do enough to unlock a well-organised and obdurate Dinamo backline.
The visitors chased an equaliser with time running out, but Croatia goalkeeper Dominik Livakovic saved Mason Mount's first-time strike and Kai Havertz's header from six yards out was brilliantly blocked by Robert Ljubicic.
It was just Chelsea's second group stage loss in 18 games, while Dinamo held on for a famous victory.
The perfect start from the Croatians gives them hope of reaching the knockout stage of the Champions League for the first time, having failed to do so in all previous seven appearances in the competition.
-- Courtesy of BBC Sport