Kyiv Dynamo faught hard to contain the Bundesliga leaders and almost managed it but an 80th minute finish from Paolo Sergio broght immense relief for the German side.
The Brazilian ran through after Carsten Jancker's header put him clear and he drove a low shot into the net to seal a win that Bayern were relieved to get.
Kyiv had recovered well from a sixth minute disaster when goalkeeepr Olexander Shovkovsky collected a corner but then dropped it to Jancker who gratefully slapped the ball into the net.
The Ukrainian champions got back into the game in the 50th minute when Serhiy Rebrov was put clear by an great through pass from substitute Alexei Gerassimenko to finish neatly under the advancing Oliver Kahn.
This defeat leaves Dynamo in danger of elimination unless they can win their next match in the section but that is not until March 1st. On the same night Bayern will play Real Madrid in the most influential game of the qualifying group.
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