The Swiss great was in magnificent form, sealing victory with a trademark backhand winner, to advance to the last eight at Indian Wells and record a third successive victory over the Spaniard for the first time.
Nadal came into the Paribas Open fourth-round encounter leading the head-to-head 23-12 but having lost January's thrilling five-set Australian Open final - and there was to be no repeat of that drama in California as Federer rolled back the years, again.
The Swiss ended a wait of more than six years to claim Grand Slam title number 18 with his win in Melbourne and his success in the desert on Wednesday night keeps him on course for a fifth Indian Wells title and first since 2012.
Next up for Federer is Kyrgios who recorded a second victory over world number two Novak Djokovic in a fortnight to reach the last eight of the tournament for the first time.
Federer will be out to avenge defeat in their only previous encounter when Kyrgios saved two match points to win a three-set epic in Madrid in 2015 that featured three tie-breaks.
Their Paribas Open quarter-final showdown could be a repeat with neither man having their serve broken this week and neither man having lost a set.
Federer rarely looked in trouble against Nadal, needing just 68 minutes to race through. Having broken his rival in the opening game of the match, Federer saved the only break point he faced in the very next game before snatching a second to lead 4-1, unleashing a fine return winner to seal the double-break advantage which he consolidated comfortably.
Nadal was unable to make any inroads in the second, and with the Spanish fifth seed serving to stay in the match at 3-5 a fortunate net-cord went the way of his opponent handing Federer two match points - he needed just one to set up his Kyrgios showdown.
"In Australia it was a very close match, I had good chances to win," said Nadal.
"Today, not. Today he played better than me. I didn't play my best match, and he played well. These kind of matches, when you're not playing your match, it is impossible to win."