The Swiss, who has won two of his last three tournaments including the Australian Open, had to dig deep to get through a second straight test after fending off a match point in his quarter-final victory over Tomas Berdych.
Australian Kyrgios, who has twice beaten Novak Djokovic over the last month, left his racket a twisted heap on the court after coming up short in a battle against the former world number one and a partisan crowd.
Federer's victory sets up a re-match of January's Melbourne Park title-decider against Spaniard Nadal, who earlier rolled over unseeded Italian Fabio Fognini 6-1 7-5.
Nadal, who lost all four of his previous Miami Open finals, will be out to snap a run of three straight defeats to Federer, including in the Melbourne final and at Indian Wells.
"Winning here would be something great, and an important title I haven't won," Nadal told reporters. "I served well (today). "That gives you calm when you have opportunities on the return."
The fifth-seeded Spaniard, with a display of powerful serving and opportunistic returns, did not face a break point against Fognini and put his opponent's serve under pressure throughout the 90-minute match.
Nadal raced through the first set in 26 minutes, losing only four points on serve while Fognini made 14 unforced errors.
"I was missing a lot of balls," Fognini said. "I give him a present of the first set. I was playing really bad."
The Italian came to life in the second set, including a stretch where he fended off five break points during his first two service games.
At 5-5, however, just when it looked as if Fognini might force a decisive third set, he double faulted and Nadal grabbed the break before sealing the match four points later.
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