Despite the straight sets win Federer was far from flawless, especially in the third set when he saw a 4-1 lead evaporate and fell 5-4 behind due to some uncharacteristically poor serving.
But he bounced back to see off the bearded Frenchman, who acted erratically throughout - screaming wildly, tossing his racket and kicking the ball after sending it into the net.
“It’s different,” Federer said of playing the unpredictable Paire, who was at times brilliant but still managed 47 unforced errors and 11 double faults in the two-hour affair.
“I’m happy to again be in the third round,” added the Swiss, who has never lost in the second round of the tournament which he has played in 18 times.
Next up for the 37-year-old is a hotly-anticipated clash with Australia’s 23-year-old Kyrgios, another unpredictable player who recovered to beat Frenchman Pierre-Hugues Herbert.
“We’ve had some brutal matches over the years. We enjoy playing against each other,” said Federer. “He has one of the best serves in the game and he’s super talented.”
Eight of the nine sets in their career meetings have gone to tiebreaks, with Federer winning two of the matches including their most recent clash at this year’s Stuttgart Open.