It was the 11th seed's first win over Selby since the 2013 Shanghai Masters quarter-final, and ended the world number one’s hopes of adding the Masters to his world and UK titles won over the past seven months.
Hawkins will face close friend Joe Perry on Saturday night for a place in the final after the ninth seed enjoyed a 6-1 drubbing of 2011 Masters champion Ding Junhui.
"It is one of the best wins of my career, probably up there with beating Ronnie (O'Sullivan) at the Crucible last year," said Hawkins. "I feel quite happy with my game at the moment. I was pleased with the way I stayed strong today.
Hawkins finishes off Selby in style at Masters
"I bounced back well after missing a couple of sore frames. They can be tough to take, but I recovered strongly."
Selby is only 7-6 clear of Hawkins in career head-to-heads illustrating the Ditton player's ability to match up well to the best the sport has to offer coming after a 6-1 drubbing of 2015 Masters champion Shaun Murphy in the first round.
Selby was philosophical about missing out on the 'Selby Slam' of world, UK and Masters.
"It would have been nice to hold all three titles at the same time," said Selby, Masters champion in 2008, 2010 and 2013. "But you've got to lose at some point, I suppose.
"I've had a great start to the season. Even though I lost today, I feel that my game is still there. I just couldn't really get into the match. The majority of frames, Barry got in first.
"I was trying to make something happen when I was getting in, but Barry would pot the red off my break-off, or else play a good safety.
'How did that go?' Hawkins shows amazing skill to pot a green
"Every credit to Barry, if he plays like that, he's got every chance in this tournament."
Hawkins will face Perry in the last four on Saturday night a year after losing 10-1 to O'Sullivan in the final here.
"Hopefully, I can get to the final, and show up a bit better than I did last year," said Hawkins. "To lose 10-1, I was completely demoralised.
I was gone in the end, and just wanted to get out of there at 7-1 or 8-1. I definitely played Ronnie last year rather than the table.
"But I felt I learned from that experience as I showed by beating him at the World Championship. This is a massive tournament, but I want to do well.
"Getting through this draw can only give me self-belief. Last year was the first time I won a match at the Masters in five attempts, but now I feel a lot more comfortable here."
Hawkins was highly impressive in carving out leads of 3-1 and 4-2 courtesy of breaks of 63, 60 and 47.
He looked to be heading for a 4-1 lead, but a safety error attempting to run safe after making 62 enabled the Selby counter-attack to close to 3-2 behind courtesy of a 71.
Hawkins maintained his two-frame lead bolstered by a 47 in the sixth frame, but breaking down on 21 in the seventh frame saw Selby run in an immaculate 101 to trail 4-3.
But he could not quite close the gap as a couple of modest scoring visits left Hawkins one frame short of victory.
Despite a wobble when Hawkins missed a red down a cushion late in the frame with the rest, Selby could not clear as he missed a tricky brown with four colours left on the table.
Mark Selby at the Masters. Chengzhe Tai/World Snooker
Image credit: Eurosport
Hawkins pounced on a long brown a few minutes later before sinking blue and pink for a momentous win over arguably the strongest player in the field.
"It was a horrible shot under pressure that brown, but lucky enough it went in and I was on the blue. I'm looking forward to doing myself justice in the semi-finals," he said.
Perry was never tested against China's leading player Ding with knocks of 55, 63, 54 and 127 setting up his first semi-final at the Masters.
"I try to play with a free mind, and I think every snooker player on the planet wants to do that," said Perry.
"Barry is my best mate, and I'd rather not play him, but at least one of us will be in the final.
The majors are what every snooker player dreams of. I've dreamt about this many times when I was younger. This feels like a home event for me.
Ding prevented the whitewash with 54 in the sixth frame, but admitted he was outplayed on the night.
Barry Hawkins (England) 6-3 Mark Selby (England)
53-27, 35-76 (76), 63-16 (63), 123-0 (60), 62-71 (Hawkins 62, Selby 71) (47) 88-0 21-101 (101) 85-0, 75-49
Ding Junhui (China) 1-6 Joe Perry (England)
32-72, 31-107 (55), 8-106, 7-67, 35-90 (63), 78-0 (54), 0-128 (127)
Desmond Kane at Alexandra Palace