Bayern Munich star Kingsley Coman scored the game's only goal in the 59th minute, with a header that Saint Germain goalkeeper Navas could not save.
Thus, Coman deprived his former team of his first coronation in the continental competition, and the second for a French club since Marseille in 1993.
The match was held in the Portuguese capital Lisbon, without fans, due to a health protocol to avoid the outbreak of the Corona virus.
This is the second time that Bayern Munich, the German champion in the last 8 years, has succeeded in defeating a French team in the final, after overcoming St. Etienne 1-0 in 1976.
France's Koeman was present at the far corner to meet Joshua Kimmich's brilliant cross pass with a header that hit the net in the 59th minute, ending a brilliant move by Bayern, who was not the best team on the field until this moment.
Coman Saint-Germain's goal punished wasting opportunities in the first half, as both Neymar and Kylian Mbappe failed to outpace Manuel Neuer, Bayern goalkeeper, from close distances, and Angel Di Maria came close to conceding the net.
Substitute Paris Saint-Germain player Eric Maxime Choubou-Moting missed two chances in the last minutes to tie the French team, who remain without achieving their first Champions League title.
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Bayern, which was founded in 1900, was contesting the eleventh final of the competition, adding a sixth title after 1974, 1975, 1976, 2001 and 2013.
Despite losing the final, Saint-Germain achieved its best journey in the competition, after reaching the semi-finals in 1995.
Bayern won all 11 matches, scoring 43 goals, but was unable to break Barcelona's record (45 goals in 2000, but then played 16 games.)
Bayern became the first champion not to lose in a single season, since Manchester United in 2008
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