The youngest player in the top 20, Thiem shrugged off the first set horror show to unleash some exquisite backhand winners in the second that had the Swiss master nodding approval.
Federer's serve was bullet-proof during the clutch moments, however, and the world number three closed out the contest with a booming ace on his second match point.
Federer, who will be contesting his third consecutive Brisbane final and is one victory away from an 89th ATP title, hailed his "best match" of the tournament.
"I really thought I hit the ball very well," the evergreen 34-year-old, lathered in sweat from the muggy Brisbane heat, said in a courtside interview.
"I'm very excited to be back in the final again... It's a great start to the season and I'm very happy."
Raonic earlier won a battle of big servers to down local contender Bernard Tomic 7-6(5) 7-6(5) in the first semi.
Both players held their serve throughout the contest but it was the Canadian who took control in the tiebreaks, jumping out to early leads on each occasion.
After Tomic won four straight points to make it 5-5 in the second set tiebreak, Raonic whipped a forehand winner down the line to bring up match point.
He closed out the contest in style, lunging for a cross-court backhand volley to end Tomic's solid run at the tournament, which included an upset win over world number eight Kei Nishikori.
"It was a great match today, a difficult one against Bernie. He's been playing so well, I know he's going to do great things this year," Raonic said.
(Reporting by Ian Ransom in Melbourne; Editing by Peter Rutherford/John O'Brien)
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