South Korea started the game brightly, forcing the first corner in the fourth minute, but were gradually forced back by an attritional Swedish side.
It was the Europeans who came closest to breaking the deadlock when forward Marcus Berg was denied by a fine point-blank save Jo Hyeon-woo in the 20th minute.
Berg was denied again nine minutes later by a desperate last-ditch block from Kim Young-gwon.
Despite their increasing dominance, Sweden also demonstrated why they have struggled to score goals.
Berg, again, and Claesson went close before the end of the half, but it was clear for everyone to see why they had only scored once in their four matches prior to Russia.
Korea threatened only on the break where Son Heung-min's pace troubled 33-year-old Granqvist, who was without defending partner Victor Lindelof, who was ill.
The somewhat rancorous build-up to the game where Sweden were accused of spying on their opponents was increasingly reflected in the niggly nature of the match.
Resilient Sweden held firm after the goal and the Hwang late scare aside, and a half-hearted South Korea appeal for a penalty, their defence rarely looked troubled.
The huge celebrations, the first match played in the $290 million stadium, at the end showed the importance the Swedes attached to this match.
Before the game, South Korea's coach Tae Yong-shin called it a "must win" game but the defeat leaves his side contemplating only an early exit.
