Captain Andreas Granqvist slotted the subsequent spot-kick with relative ease to net the only goal of the game in what was an evenly fought Group F encounter that could have swung either way.
Sweden had not scored in three outings prior to the tournament but they showed the greater attacking intent in the first half.
South Korea XI: Cho Hyun-woo, Lee Yong, Kim Young-gwon, Jan Hyun-soo, Park Joo-ho; Kim Shin-wook, Koo Ja-cheol, Ki Sung-yueng, Lee Jae-sung; Hwang Hee-chan, Son Heung-min.
Sweden next face Germany, while Korea take on in-form Mexico who pulled off a major shock by beating the world champions in their Group F opener. The Swedes will next face the Germans on Saturday, while South Korea plays Mexico on the same day.
It was the third penalty to be awarded because of a video review in the first 12 games at this year's World Cup.
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.More news: Villagers recover woman's body swallowed by giant python in Indonesia
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The video review system, making its World Cup debut in Russian Federation, appears to be working so far.
In a scrappy game, Cho also saved well from Ola Toivonen's header following a free-kick.
And after VAR intervention, they were handed the chance of breaking that run and a nervous looking Granqvist stepped up, tucking the ball into the bottom to score his side's first goal at a World Cup since 2006. Hwang is unmarked at the back post to meet a devilish corner from the left, but he inexplicitly heads wide from a matter of yards out.
That proved the telling blow and Sweden were largely untroubled as they saw out victory.
Sweden were in control of the match in the opening 45 minutes and created a couple of good openings, neither of which they were able to take.
Sweden couldn't afford to miss the chance against a struggling South Korea team with tough challenges against Germany and Mexico next.
Andersson's counterpart, Shin, a former star for the national team as a player who rose up the ranks after coaching South Korea's youth teams, seemed to take the whole thing in stride.
Sweden's starting players averaged about 1.90 meters (6-3), while South Korea's starters averaged about 1.83 meters (6 feet).