Coutinho looked set to score from open play in the 59th but was brought down by Kingsley Ehizibue, who was sent off for Cologne. Coutinho later set up Ivan Perisic in the 73rd as Bayern moved second, two points behind early leader Leipzig, which defeated injury-hit Werder Bremen 3-0 in the late game.
Lewandowski grabbed the first two goals to take his league-leading tally to nine in five games. Cologne was already finding its Bundesliga return difficult with three defeats in four games, and any hopes the promoted side had of bucking the trend were given short shrift when Lewandowski got Bayern off to a flying start in the third minute.
The Poland striker matched Carsten Jancker's record of scoring in the first five league games of the season for Bayern. Jancker managed it 19 years before. The visitors were unable to keep up with the home side's pace. Coutinho, who was leading Bayern's attacking play, struck the post with a free kick.
Cologne regrouped toward the end of the half but couldn't force an equalizer. Lewandowski grabbed his second in the 48th with a header from a corner, before Coutinho went on to steal the limelight. FIRST HERTHA WIN
Javairo Dilrosun scored a brilliant solo goal as Hertha Berlin defeated fellow struggler Paderborn 2-1 for its first win of the season. The Dutch winger said afterward he did not know how many Paderborn defenders he passed before opening the scoring in the 10th minute.
"I'll have to look at the replay," Dilrosun said. Hertha's plan was to let the visitors have the ball and then hit on the counterattack. But Ante Covic can't have anticipated his side would allow so many chances. Hertha goalkeeper Rune Jarstein ensured it remained 1-0 ahead at the break.
Marius Wolf scored his first goal for Hertha in the 52nd, prompting a streaker to venture onto the pitch. The home fans' celebrations continued as stewards went to catch him. Perhaps distracted, Hertha allowed Ben Zolinski to pull one back for Paderborn two minutes later.
But the home side improved, had two goals ruled out for offside, and ultimately held on to move level on four points with city rival Union Berlin. Union lost 2-0 at Bayer Leverkusen, which was keen to atone for its loss to Lokomotiv Moscow in the Champions League on Wednesday.
Also, Augsburg salvaged a 1-1 draw at Freiburg.
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