Oshoala struck 15 minutes from the end with a super burst and finish to seal the win after a comical own goal from Kim Do-yeon, who somehow hooked a long ball back past onrushing goalkeeper Kim Min-jung, had put Nigeria ahead in the 29th minute.
Swede Dennerby was full of praise for the lightning quick 24-year-old after a huge win, just their second in the World Cup since 1999.
"She's very special because no-one has the speed she has," the 59-year-old told reporters.
"It's important for the team because you can create a chance from nothing, even a clearance can be a goalscoring opportunity."
The hard-fought victory for Dennerby's side left the unfortunate South Koreans pointless after their first two games in Group A and put Nigeria level with France and Norway on three ahead of their crunch clash in Nice later on Wednesday.
Nigeria can now legitimately hope for a place in the last 16 regardless of what happens in their last group match against the tournament-hosting French.
Four third place finishers from the six groups will qualify, meaning three points could well be enough to see the Super Falcons through to the knockout rounds for the first time since 1999, when they reached the quarter-finals in the US.
However Dennerby is targeting a result against France in Rennes on Monday to remove all doubt.
"France are a very good team, if we come out of that with one point we'll all be very happy," Dennerby added.
South Korea meanwhile face an uphill task to go through as they face a strong Norway side in their final group match next week, after watching Lee Geum-min's strike ruled out for a very tight offside just before the hour mark.
Later, Group B leaders Spain face off against strongly-fancied Germany in Valenciennes, with the two sides locked on three points and aiming to secure qualification with a game to spare.
The Germans are missing star playmaker Dzsenifer Marozsan, who has been ruled out until at least the end of the group stages after breaking her toe during her side's 1-0 win over China on Saturday.