Jamal Musiala, the youngest Bayern player to reach 100 Bundesliga matches, headed the visitors into the lead after a pinpoint cross from Thomas Mueller in the 33rd minute.
Kane then powered an unstoppable shot from 20 metres out into the top corner for his 21st league goal two minutes before the break.
The England captain has now been involved in 26 goals in the league with his 21 goals and five assists, equalling the tally for the entire 2022/23 season of Randal Kolo Muani, who had the most goal involvements.
Wolfsburg, however, still had time to cut the deficit after Maximilian Arnold was given too much space at the edge of the box to beat keeper Manuel Neuer with his shot.
The Bavarians soaked up considerable pressure and Neuer blocked another Arnold shot in stoppage time to protect their lead.
Bayern are in second place on 38 points with a game in hand and with leaders Bayer Leverkusen on 42.
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