
The number 109 winner blasted 15 aces - including two runs of four aces in the same game - as he pounced on the underdone top seed in draining, 43-degrees Celsius conditions.
The American seed complained of feeling unwell and made two brief trips to the locker room.
It was Roddick's second collapse in a month after failing to finish off Richard Gasquet in a Wimbledon semi while leading two sets to love.
The winner of two previous Indy editions was furious with his lacklustre showing.
"I didn't have much to give out there today," Roddick said. "I don't know why I wasn't feeling that well. I served badly, but I've been doing that all week. I don't know what happened."
Dancevic, 22, continued to break new ground for Canada as he played the first ATP semi-final for the nation since Sebastien Lareau six years ago in Memphis.
He will face off Sunday against Russian third seed Dmitry Tursunov, who beat Californian Sam Querrey 7-6 (7-5), 6-2 in a semi.
Earlier, Querrey fired 34 aces - including nine in a row - to defeat holder and second seed James Blake 7-6 (10-8), 6-7 (4-7), 7-6 (7-4), reaching a first career final-four place.
In his first match of two on the day, Tursunov beat defeated number 373 amateur Kei Nishikori 6-1, 6-4 in another quarter-final held over due to Friday rain.
Dancevic won the first set against Roddick on a break, lost a break midway through the second but finished his last three service games with untouchable serves.
He dominated in the tiebreaker to complete the upset.
The last man into the draw by ranking was still coming to grips with his accomplishment.
"I haven't thought about being in the final," said Dancevic. "I'm just enjoying the moment. My game plan was not to get broken. I didn't want to get behind against him. It seemed that when I got stressed out, I would hit a few good shots and win the game."
The last Canadian to win an ATP title was Greg Rusedski in 1995 in Seoul, just months before he took British citizenship.
Querrey, who lost seven matches in a row on clay and grass this spring in Europe and Britain, was stunned by his serving prowess.
"It was one of those days when I was just in a zone serving, and it definitely paid off there at the end," he said. "But for me, beating a top-10 player is more important than reaching the semi- finals."
Blake has not won a title since the first week of the year in Sydney, after lifting six trophies in 2006.
"I wish I had more matches here, but I only lost a set this week." said Blake, who had won his previous seven matches at Indianapolis.
"I've played a few matches these last two weeks at events where I also could have lost early. I'm still high on confidence. I just need to keep my fitness and get ready for the Open (starting August 27)."
DPA