Van Der Breggen gapped Hall by around nine seconds on the descent from the penultimate climb but with one kilometre to go on the final uphill, Hall caught and passed the reigning Olympic champion, crossing the line 21 seconds ahead.
The American took advantage of her home soil knowledge when she saw Van Der Breggen start to struggle.
"I've raced here at altitude a couple of times and I'm not sure she's raced at altitude a tonne here," Hall said.
"But I know if you dig too deep you can explode pretty completely. I kind of saw her slowing her down and thought 'it's my time to go!"
"Yeah, I'm a little surprised. I had no idea what to really expect here but I do like the long climbs so we went into the day with the attitude "let's give it a try and see what we can do."
"Boels-Dolmans is the best in the world but it doesn't mean we can't try."
The pair broke free from what remained of the bunch on the crest of the penultimate climb where Van Der Breggen blew the race apart for overnight race leader and team mate Megan Guarnier. Just 10 riders remained - including two UHC riders and Guarnier - when Hall attacked, Van Der Breggen sticking to her wheel initially on police duties.
The duo quickly gained a 20 second lead over the peloton on the descent, both comfortable knowing they had the numbers behind if the cards didn't fall their way.
Like stage 1, Boels-Dolmans also dominated today's 108 kilometre stage. Other than an early attack by Juliette Labous (Sunweb) who returned to the peloton after the first climb, the team's control of the race was technically perfect. But like Van Der Breggen admitted after the stage, not everything goes according to plan.
"You can always make a plan and you have to see how it goes in the race," she said. "We tried our best and i think we couldn't have done more to win, Katie was just too strong.
"I had to make it up to the finish that was mostly the thing in my mind! It was tough especially when you do a climb like that and attack on the bottom of this climb it's difficult to have that final punch.
"Of course Katie was really strong today so it was good to have a bit of a gap before the final climb but I don't know what she eat before that climb," she joked.
Hall now holds a three second overall lead over the Dutchwoman.