Mueller's strikes proved the breaking point for Haifa, who, even after van Buyten scored the first in the 64th minute, tried valiantly to make inroads into the Bayern defence and came close on two occasions.
Bayern dominated possession save for a 10-minute period at the beginning of the second half and it proved enough as the Germans eventually wore down Haifa's tiring defence.
In the first half, Haifa defended bravely with Bayern's Ivica Olic heading the ball into the net in the 26th minute but it was ruled offside.
Haifa keeper Nir Davidovitch made a fine diving save to keep Bayern at bay in the 57th minute when Arjen Robben shot low and hard after a free kick.
Van Buyten finally broke the deadlock when the Haifa defence failed to deal with a corner which fell to the giant defender who blasted his shot past Davidovitch.
Haifa's Vladimer Dvalishvili had his side's best effort when his shot from the edge of the area in front of goal was tipped over the bar by Bayern keeper Hans-Joerg Butt in the 76th minute.
Mueller was then allowed space on the edge of the area and he blasted the ball in after a cross in from the left in the 86th minute.
He sealed the win two minutes later when a sharp cross from substitute Mario Gomez landed at his feet and he tapped in from close range.
Bayern coach Louis van Gaal said he was delighted to get off to a positive start.
"I was very satisfied about the first half. We played at a very high tempo."
He added that Haifa could not keep up with Bayern's pace. "After we scored the first goal, it was easy for us," the Dutch coach said.
Haifa coach Elisha Levy said that the scoreline was not a true reflection of the match.
"After we went 1-0 down we went for broke and tried to equalise but at this level you must be patient to the end. The 3-0 scoreline does not tell the full tale of events during the match," he said.
Despite the convincing defeat, Haifa's players received a healthy round of applause from the almost capacity crowd of 39,000 spectators on a sultry evening at the National Stadium in Tel Aviv.
Haifa are playing their home matches in Tel Aviv, about 100kms south of their home base, because their ageing stadium is not fit to host matches at Champions League level.
