Bayern's trajectory starkly contrasts with that of BVB, who have seen their five-point lead after seven matchdays vanish and their hopes of Champions League progression all but dashed amid a run of just one win in seven in all competitions.
James Rodriguez brought a sublime cross from Thiago Alcantara - in as one of four changes from the side that beat Celtic 2-1 in the Champions League in midweek - down on his chest at the back post before laying off for Robben to pick out the top-left corner with a sweet strike from just inside the box.
Bayern Munich next face FC Augsburg in two weeks time and will be looking to extend their league at the top of the German league. "We are not the ones under pressure".
Dortmund's evening got even worse before the end of the first half due to Sokratis Papastathopoulos limping off injured, but they could so easily have been back in the match had Yarmolenko got the better of Ulreich in his second clear-cut chance of the contest.
"He has not sustained an injury, but an overburdening", Heynckes said.
Dortmund were more than happy to sit off their opponents in the opening 45 minutes and cede possession, which initially looked to work well enough as they were given the chance to counter-attack.
Forward Timo Werner set up a goal and scored a late victor himself as Leipzig battled from a goal down against Hanover.
Dortmund nearly reduced the lead further, but Gonzalo Castro missed a chance at the far post to ensure Bayern's dominant performance deservedly earned all three points.
Six wins from their first seven matches were then followed by a sudden slump in form and two losses and a draw in their last three games.
Elsewhere Schalke, who are now undefeated in their last six games in all competitions, climbed to fourth - level on 20 points with neighbours Dortmund - with a 1-0 win at Freiburg.
"It is my job to give my players their confidence back", said Dortmund coach Peter Bosz. They created close to a dozen scoring chances against the Cypriots on Wednesday but were let down by poor finishing.
"There are going to be tough times, and right now is a tough time - but I believe in our team and I think we can bounce right back". "At the start of the season when we were winning points, expectations were high".