Kroos let fly to the top left corner with 14 minutes remaining, just as a defensive Valencia side had threatened to equalize Bastian Schweinsteiger's 38th-minute opening goal.
"Of course it's always dangerous when it's 1-0. The second goal was very important for us," Schweinsteiger said.
Valencia substitute Nelson Valdez out-jumped two Bayern markers in injury time to head Jonathan Viera's cross beyond goalkeeper Manuel Neuer for some late drama.
There was still time for Valencia defender Adil Rami to earn a second yellow card for bringing down Arjen Robben in the penalty area, and for substitute Mario Mandzukic to miss the resulting penalty on his Champions League debut.
"Valencia played on the counterattack but hardly had any chances," said Bayern coach Jupp Heynckes, whose side had 74 percent of the possession and 17 efforts on goal compared to the visitors' four.
"You have to be critical about the end. It shouldn't happen to a team that it feels so secure. We lost concentration."
Belarusian champion BATE Borisov won 3-1 at Lille in the other Group F match.
Bayern's previous Champions League game in Munich was last season's final.
The Germans sought to brush away memories of that painful defeat on penalties to Chelsea by seizing the initiative against Valencia, which it beat on penalties when last winning the competition in 2001.
Franck Ribery overcame muscular problems to play and caused headaches in the Valencia defense before he went off injured at halftime.
The Frenchman flashed his volley wide from corner in the 11th, and was inches from meeting Robben's cross minutes later. Schweinsteiger's following effort was easily gathered by Alves, moments before Kroos drew a smart save from the Brazilian goalkeeper.
Valencia's injury-hit side packed nine outfield players behind the ball, forcing Bayern to be patient as it sought a way through.
"Sometimes it's a game of patience, when you know how the opposition plays," Heynckes said.
Record signing Javi Martinez made his first start for the home side, and the ¤40 million man looked assured as he snuffed out what little Valencia offered in attack, while driving on his teammates for the opening goal.
When it came, it was after a rare Valencia foray forward. Ribery made the break before Robben set up Schweinsteiger for a shot that took a slight deflection from Aly Cissokho and nestled inside the far post.
The goal spurred the visitors into seeking a response and Tino Costa had their first effort on target in the 52nd, though it was easily dealt with by Neuer.
Moments later, Kroos' appeals for a penalty were ignored after he tumbled under Antonio Barragan's challenge.
Feghouli burst through five minutes later, only for Ricardo Costa to stray offside, and the Valencia midfielder went even closer in the 67th when he was forced out for a corner.
Bayern was struggling to impose its authority as it had in the first half and the fans were getting restless until Feghouli, arguably Valencia's biggest threat on the night, lost possession and Holger Badstuber found Kroos to make the game safe.
"Disappointed, yes. But not despondent," said Valencia coach Mauricio Pellegrino, who missed the decisive penalty in the 2001 final. "We didn't threaten their goal much, but when we did, we did it well."
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