Sweden will next face reigning champions Germany in Sochi on Saturday.
The best three chances fell to Marcus Berg but he was denied by a combination of good goalkeeping, last-ditch defending and uncertainty in front of goal. The ref had initially waved play on. Sweden had a chance with a corner in the 43 minute but it was saved comfortably.
It wasn't a flowing performance from Sweden, but securing the win will come as a huge relief to Andersson and his team.
Indeed, Janne Andersson's team looked to be heading for a goalless draw until the second-half penalty.
The Swedes saw the rest of the game out with relative ease and have given themselves a real chance at qualifying from the group.
Sweden were just about good enough, but it wasn't exactly an inspiring display.
Sweden had been accused of spying on a Korea training session ahead of the game.
Thousands of "Red Devils" South Korean fans, many clad in the team's signature scarlet and chanting "Go Korea!" gathered at major thoroughfares and football stadiums across the country to watch the opening game.
However, they arrived in Russian Federation without a goal in their previous three matches and without Zlatan Ibrahimovic after his retirement from global football.
The Swedish group may be stronger without Ibrahimovic, and the fact that this was largely the squad that earned qualification is worthy of respect. 2018 FIFA World Cup Group F Points Table. Sweden was effective in breaking up any chance of rhythm with fouls.
Korea's gameplan had focused on negating Sweden's physicality and coach Shin Tae-yong conceded they may have become too preoccupied with that issue. It was a novel tactic.
Neither history nor statistics are in South Korea's favour when it comes to their meeting with Sweden. It may well be a little unfair to heap all the weight of expectation and responsibility onto the shoulders of one player.
Against Sweden, he was wasted.
Some of the Swedish players deserve an Oscar or at the very least an Olympic gold medal for diving as the team struggles to come to terms with the post-Zlatan era.
Although South Korea failed to get a promising result in the end, it was Jo who at least the kept the game a one-goal affair.
He did get a chance to burst down the right in the 35th minute and sent in a risky cross, but there was very little of note from the 25-year-old apart from that.
Andersson says the 36-year-old is now firmly out of the picture when it comes to Sweden's plans and has not had any involvement at any stage of the build-up to Monday's match in Nizhny Novgorod.
Tom Marshall covers Liga MX and the Mexican national team for ESPN FC.