Manchester City had threatened twice before a close-range strike by Bayern’s Serge Gnabry’s was disallowed by a narrow offside call in the seventh minute.
Five minutes later Haaland struck. After Riyad Mahrez’s free kick was blocked Kevin De Bruyne managed to corral the ball and slip a pass through for Jack Grealish, who whipped it across to Haaland to connect from close range.
Frustratingly, another round of electrical storms brought proceedings to a halt, with players exiting the field and the near sellout crowd of 78,128 at the iconic home of the NFL’s Green Bay Packers instructed to seek shelter in the concourses.
The start of the match had already been delayed almost 20 minutes because of dangerous weather conditions.
The disruptions didn’t dampen the festive atmosphere for the first professional soccer match ever held at Lambeau, with a few hardy fans even braving the pounding rain and risk of lighting to remain in their seats during the stoppage.
Play resumed with 27 minutes left to complete a 40-minute first half and Haaland quickly energized City fans in attendance, bursting through behind the Bayern defense.
But before he could unleash a shot a charging Dayot Upercampo booted the ball away.
Although Manchester City controlled the pace, Bayern had a golden opportunity in the 38th minute when a cross from the right found Alphonso Davies at the far post, but his pass across the goal face didn’t quite make it to Gnabry.
A minute later Haaland almost made it 2-0, but his left-footed shot from inside the area was disallowed for offside.
Haaland departed after 40 minutes of action, giving way to newly signed striker Julian Alvarez who nearly doubled the score in the 43rd.
Despite a stream of substitutions in the second half, tension remained high between the Premier League and Bundesliga champions until the end of the truncated contest as Bayern -- who opened their brief tour with a 6-2 drubbing of Wayne Rooney’s DC United, sought in vain for an equaliser
Both clubs were flying home after the match, with Manchester City due to take on Liverpool in the Community Shield next Saturday, when Bayern face RB Leipzig in the SuperCup final.