The Italian outfit finished 12th in Serie A last season and promised a tough test for Malky Mackay’s Premier League newcomers.
However, South Korean Kim proved the difference as he fired home after 57 minutes to give the home side a morale-boosting victory.
Cardiff began the game with new signing John Brayford in the side and record signing Steven Caulker on the bench.
The match started slowly and the first chance did not arrive until 32 minutes, when Chievo’s Alberto Paloschi rounded goalkeeper David Marshall after seizing on Peter Whittingham’s poor backpass, but he saw his shot cleared off the line by Ben Turner.
Paloschi once again went close soon after when he rose to meet an inswinging corner from the left, but his header flew over.
Tommy Smith responded for Cardiff, shooting wide from the edge of the area, before Craig Noone’s snapshot flew over the crossbar as the first half drew to a close.
Cardiff began the second period with plenty of purpose, and Whittingham and Kim both had early chances well saved by Marco Silvestri as the Welshmen took the game to their opponents.
Silvestri could do nothing to prevent Kim giving Cardiff the lead a few minutes later, though, when he fired home the rebound after Noone’s effort had been saved.
Chievo’s players protested that there had been a foul during the build-up to the goal, but the referee disagreed and waved away the appeals.
The biggest cheer of the day came when Caulker was introduced with 30 minutes remaining, replacing captain Mark Hudson in the centre of Cardiff's defence.
The game became increasingly open as both sides made a succession of changes, and substitute Joe Ralls nearly extended Cardiff’s lead as he hit a right-footed shot on the turn, but substitute goalkeeper Lorenzo Squizzi saved well.
Chievo were unlucky not to equalise with 10 minutes remaining, Paloschi hitting the post from the rebound after his initial effort had been saved by Marshall.
Riccardo Improta then went close for the visitors as they searched for an equaliser. The Italy Under-21 international let the ball run across his body, before hitting a left-footed shot on the turn that drew a full-stretch save by Marshall.
There was still time for Caulker to come close to a debut goal, but his header from Whittingham’s cross flew over the Chievo crossbar.