The big moment in the match arrived little over an hour in as the use of video technology saw referee Joel Aguilar pull play back and award Janne Andersson's charges a spot kick, from which Granqvist converted to send his side joint-top of the standings.
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.
Kim Young-gwon produced two impressive blocks inside the area to deny Marcus Berg and Granqvist, the latter of whom also shot straight at third-choice keeper Cho Hyun-woo towards the end of the first half.
Cho then stood firm to keep out Berg's effort from close range in the best chance of a first half that never truly got going, as Sweden's inability to convert - three goals in seven games prior to this one - threatened to haunt them.
Sweden's breakthrough goal eventually arrived 25 minutes from time thanks to the use of VAR, which saw referee Aguilar correctly rectify his initial call when substitute Kim Min-woo lunged in on Claesson inside the box.
Centre-back Granqvist nominated himself to take the penalty kick and rolled it to Cho's left, sending the goalkeeper the wrong way in the process.
Korea, competing at the World Cup for a ninth successive time, lacked an attacking threat all afternoon and barely offered anything in response.
The Taeguk Warriors' only other chance fell the way of Hwang Hee-chan, who planted a header over the crossbar from a promising position late on.
SWEDEN (4-4-2): Olsen; Lustig, Granqvist, Jansson, Augustinsson; Larsson (Svensson 81'), Ekdal (Hiljemark 71'), Forsberg, Claesson; Berg, Toivonen (Thelin 77')
SOUTH KOREA (4-3-3): Cho; Lee, Jang, Y.G Kim, J.H Park (M.W Kim 28'); Koo (S.W Lee 73'), Ki, J.S Lee; Son, S.W Kim (Jung 66'), Hwang