It was a vital victory for Germany, keeping their campaign alive after being held to a scoreless draw by Brazil in their opening match.
The tournament favourites had targeted winless Nigeria for a decisive and confidence-building victory but instead were unable to put a sound game together.
Despite Germany fielding a vastly experienced squad, all veterans of last year's World Cup triumph, the match degenerated into an episode of wayward passes that lacked cohesion.
The sole goal came in the 64th minute when Stegemann latched on to a cross from Anja Mittag who had found space to move down the left flank and slammed the ball past goalkeeper Precious Dede.
However, only desperate measures by goalkeeper Nadine Angerer spared Germany from what could have been a shock loss.
In one move she saved twice in quick succession diving left to deflect a shot by Sarah Michael then picking herself up in time to punch away a blinding shot from Perpetua Nkwocha who had latched on to the rebound.
Germany's remaining game is against North Korea, and although they are not playing up to the standard that saw them win the World Cup last year they should still qualify.
The second loss for Nigeria has put them out of contention.