The German champions stretched their record run to 15 straight wins in the competition, with Robert Lewandowski firing in on the rebound in the 43rd minute after the hosts had struggled with Salzburg’s high-intensity pressing during the first half.
Lewandowski now has 71 goals in the competition and is joint third-best scorer of all time, along with Spaniard Raul, behind Lionel Messi and leader Cristiano Ronaldo.
The Austrians had started much stronger, putting the hosts on the back foot, and would have been ahead in the 16th minute were it not for keeper Manuel Neuer’s superb double save.
“It is very important that we are already now confirmed group winners,” Neuer said. “It is a clear step in the right direction.”
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Bayern, who slipped up in the Bundesliga with a draw against Werder Bremen on Saturday, were lacking their usual spark and got lucky in the 52nd minute when Salzburg defender Maximilian Woeber deflected Kingsley Coman’s shot into his own net.
Bayern were left with 10 men in the 66th following the dismissal of Marc Roca with a second booking but two minutes later Leroy Sane settled their nerves, heading in their third goal.
Salzburg cut the deficit through Mergim Berisha in the 73rd after Neuer had pulled off another sensational double save minutes earlier.
The Bavarians, who have now scored two or more goals in all four of their group games, top Group A on 12 points, with Salzburg in last place on one. Atletico Madrid are second on five following their goalless draw with Lokomotiv Moscow, who have three.