Returning from a wrist injury, Nadal took the first set but momentum swung at 3-3 in the second when Raonic claimed four straight games.
Raonic capitalised on an early break in the decider and served out to book a semi-final against Dimitrov who beat Austrian Dominic Thiem 6-3 4-6 6-3.
"It was a great match tonight and I'm very happy with myself, how I competed against such a great player and competitor as Rafa," Raonic said in a courtside interview.
Raonic fired down 19 more aces than Nadal.
"That's six games I got for myself without having to run too much, which is very generous of myself," he added.
Nadal, returning to the tour this week after injury, struck 19 winners as he continued his preparations for this month's Australian Open.
"He was more aggressive than me... but I take the positive. It was a small difference," said the Spaniard who had added former world number one Carlos Moya to his coaching team last month as he seeks to revive his career following a spate of injuries.
World number four Stan Wawrinka survived aggressive hitting from Briton Kyle Edmund before winning 6-7(2) 6-4 6-4 in another quarter-final.
Edmund cruised through the first set tiebreak before Wawrinka, making his Brisbane debut, raised his game to beat the world number 51.
Swiss Wawrinka will meet Kei Nishikori in the semis after the Japanese third seed's 6-1 6-1 win over local favourite Jordan Thompson.
(Reporting by Amlan Chakraborty in New Delhi; editing by Ed Osmond)
