The South Koreans are next in action against Mexico on Saturday, before finishing off their group-stage campaign against Germany on June 27.
For all their superior possession numbers early, South Korea made just one shot attempt, and none on target, in the first half, while Sweden had eight attempts, with two on target.
He produced a brilliant save in the 20th minute to deny Marcus Berg from point-blank range, before recovering well to prevent the Swedish striker a follow-up opportunity.
The all-action Kim was in the thick of the action again soon after, throwing himself in front of Berg's scuffed effort from a corner, while Claesson saw a header deflected narrowly over on the stroke of half-time.
The referee is having a look at the video replay.Sweden have a flawless chance to take the lead.
Andreas Granqvist netted from the penalty spot in the 65th minute after the video assistant referee was called into action to give Sweden a potentially crucial victory even without the retired Zlatan Ibrahimovic. Captain Andreas Granqvist slots it away!
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South Korea's star player, the Tottenham forward, Son Heung Min had a quiet first half with just one half-hearted shout for a penalty.
South Korea were now struggling to stay on level terms and were forced to make a change on 27 minutes when Park Joo Ho was taken off and replaced by Kim Min Woo. Follow the blog to get all the latest updates from Sweden's Group F Opener!
Sweden, which is playing without the retired Zlatan Ibrahimovic, beat Italy in the playoff round to deny the Italians a World Cup spot for the first time since the 1958 tournament and secure their own place in Russian Federation.
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In World Cup warm-up matches, he switched the numbers of his players around, arguing Swedish scouts would be confused because he says "it's very hard for westerners to distinguish between Asians". Berg is coming off the back of a fine domestic season, scoring 25 league goals for Al Ain in the Arabian Gulf League.
Sweden picked up the three points, but it wasn't a display that instilled confidence, although perhaps being more on the back foot against Germany and Mexico may suit them.
It was the third penalty to be awarded because of a video review at this year's World Cup.
And if you're South Korean coach Shin Tae-yong, you figure out how to work that to your advantage. Son's electric pace is going to be a valuable asset for his side, who will be looking to break down a stubborn Swedish defence.