The Brazilian's 18th-minute shot, which was deflected past goalkeeper Koen Casteels by Wolfsburg's Luiz Gustavo, was enough for Bayern to beat the toothless Wolves, who did not register a shot on goal for 82 minutes.
Despite controlling possession, however, Bayern never hit top gear and failed to kill off the tie, with forward Robert Lewandowski looking desperately alone up front.
Bayern defender Mats Hummels should have done better when he was twice left with too much space in the box but headed wide both times.
The hosts were almost punished late in the game when Yunus Malli and Daniel Didavi had a chance each with Bayern keeper Manuel Neuer keeping his cool to deny them from close range.
Hamburg SV also booked a spot in the quarter-finals, beating Cologne 2-0 to underline their improving form.
Gideon Jung tapped the ball over the line after Cologne keeper Thomas Kessler palmed a shot into the 22-year-old's path in the fourth minute.
Hamburg, who are in the Bundesliga's relegation playoff spot, hit the woodwork through Luca Waldschmidt before Bobby Wood made it 2-0 in the 76th after a powerful run.
Hamburg have won their last two matches, having also beaten Bayer Leverkusen in the league on Friday, and notched their fourth consecutive home victory in all competitions.
Borussia Moenchengladbach also eased into the last eight by beating second division Greuther Fuerth 2-0.
Last year's finalists Borussia Dortmund host Hertha Berlin on Wednesday.
RESULTS
Hamburg 2 (Jung 5, Wood 75)
Cologne 0
FCA Walldorf 1 (Carl 78)
Bielefeld 1 (kSchuetz 53) aet
Bielefeld won 5-4 on penalties
Bayern Munich 1 (Costa 17)
Wolfsburg 0
Greuther Fuerth 0 Borussia Moenchengladbach 2 (Wendt 12, Hazard 36-P)
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