Bayern down dogged Romans
Last season's Champions League runners-up, who have only scored twice in three league games so far this season, squandered a half dozen chances but stayed patient against a toothless Italian side that paid the price for their defensive approach.
"We let the ball run and allowed little against a defensive team but after 70 minutes they just ran out of steam," said Bayern coach Louis van Gaal.
"So when a team like Roma stays behind the ball with 10 men then we need time to break this team and that is exactly what we did," he said.
Thomas Muller broke the deadlock in the 79th minute with a well-taken shot from the right and substitute Miroslav Klose doubled the lead when he snuck in to connect with a Holger Badstuber free-kick.
Without injured Arjen Robben and suspended Franck Ribery, Bayern were made to work hard in the first half as the Italians stifled their attacks by getting men behind the ball.
But the Germans, who had been dominating possession, turned up the pressure in the second half and went close through Toni Kroos and Mueller.
Bayern coach Louis van Gaal brought on strikers Klose and Mario Gomez after 67 minutes to add punch and the move paid off.
Roma keeper Julio Sergio made a series of spectacular saves to keep his team in the game but could do nothing when Muller cleverly whipped a shot from the edge of the box onto the far post and into the net for a deserved lead. Klose had earlier headed against the post.
"We did it with patience," said midfielder Bastian Schweinsteiger. "We wore them down and got them ready for the second half when we created the chances. They were getting more and more tired."
Klose secured the points seven minutes from time, flicking in from close range after Roma's Marco Boriello was denied by Bayern keeper Jorg Butt from close range in the Italians' only real chance of the game.
"We are largely satisfied with our performance tonight though the result does not accurately reflect the game," said Roma coach Claudio Ranieri. "We did have our chances but Bayern converted the ones they got."