The home side were leggy and lethargic for most of the evening, as a well-drilled Dortmund, knowing they would endure long period without the ball, dropped deep in a bid frustrate to Pep Guardiola's side.
BVB even threatened to walk away with a shock away win, as Jude Bellingham cleverly guided Marco Reus' cross past Ederson just before the hour mark.
But after Stones had rocketed City level, with an effort that Alexander Meyer should really have saved, Haaland stepped up to score his 13th goal of the season - meeting Joao Cancelo's stunning cross to divert the ball home from six yards out.
The first half at the Etihad was anything but what you'd expect. Dortmund were compact and organised at the back - and mildly dangerous on the counter - whereas City were toothless in attack despite enjoying the lion's share of possession.
Dortmund's control of proceedings was highlighted by the fact that Erling Haaland touched the ball just 11 times in the opening 45 minutes - comfortably the fewest of any home outfield player and five less than Ederson.
Kevin De Bruyne was also ineffective in the opening period as the visitors' low block restricted the half spaces that the Belgian tends to operate in, although Guardiola neglected to make any changes at the break.
But rather than get any better, like things so often do when City have a poor first 45, things took a turn for the worse just before the hour mark.
Giovanni Reyna's corner was half cleared and Reus, who should really have given Dortmund the lead minutes earlier after a blistering counter attack, controlled neatly before guiding the ball back into the danger zone.
There stood the alert Bellingham, who was brilliant throughout the evening, and he nipped in front of former Dortmund defender Manuel Akanji to nod past a helpless Ederson in the City goal.
Guardiola immediately introduced Julian Alvarez, Bernardo Silva and Phil Foden into the game, for the ineffective trio of Jack Grealish, Riyad Mahrez and Ilkay Gundogan, but they weren't able to make the desired immediate impact as Dortmund stood firm.
However, City never know when they are down and out, and with 10 minutes remaining the game turned on its head. First, Stones gathered De Bruyne's pass to unleash a rocket into the top corner from 25 yards out, before Cancelo whipped a superb cross into the box that the lively Haaland was quickest to get on the end of.
It was harsh on Dortmund, who were far more organised than many would have expected before the game, but Edin Terzic's side walk away with nothing from a spirited performance.
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