A Lisa Dahlkvist goal was enough to separate the two teams in a hard-fought contest that swung both ways over the 90 minutes, but Sweden eventually made their superiority in creating chances count with the only goal of the game.
The first half was a very even affair, although you could sense the nerves with both teams desperate to pick up the three points.
All the best chances of the opening 45 minutes fell to Lotta Schelin, the first of which was after just three minutes as she burst into the penalty box from the left-flank but snatched at her shot and watched it fly over the bar.
Twice more the Lyon forward found herself clear in the area in the first half and she hit her efforts wide of the post on both occasions, making her day a very frustrating one in the early stages.
Most of Korea DPR's threat came from the right thanks to the duo of Song Jong Sun and Kim Su Gyong, but they couldn't quite find the final ball to break the deadlock.
It was this pair who produced Korea DPR's best early effort though as a Song cross found the head of Kim, who had made a rare move into the middle, but her effort ended up well wide.
As the teams returned for the second period it seemed to be more of the same but Sweden got the first good chance of the half as Schelin broke the offside trap and played in Dahlkvist, but she was stretching and couldn't quite get to the ball in time to slot it past Hong Myong Hui.
Just ten minutes later it was Dahlkvist who did break the deadlock after a period of sustained pressure from the Swedes.
Korea DPR hadn't reorganised after a corner and Linda Forsberg swung in another cross from the left to find Therese Sjogran at the back post. She was calmness personified as she slid it back across goal to Dahlkvist, who controlled and slammed the ball home.
Korea DPR continued to work hard to get back into the game and came closest through Ri Un Hyang who made the most of Hedvig Lindahl's flap at a cross to head the ball goalward, but there was Sara Thunebro on the line to make the clearance.
Sweden controlled the latter stages well and showed their extra experience to close out the game. They will reach the quarter-finals if United States do not lose to Colombia later on Saturday.
Korea DPR need Colombia to win to have any chance of progressing.