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Paire looked all at sea in losing the first set against Australian John Millman, and when he faced a break point early in the second his chances were looking forlorn.
But he reeled off five consecutive games from there to level, then took the third for a 3-6 6-1 6-4 victory in one hour 42 minutes.
The 30-year-old Paire is the ultimate showman, but exhibited his gritty side to sway the momentum.
"When I was served the break point at 1-1 I was a little bit more aggressive, more offensive," said Paire. "It helped me to come to the net and then I broke him with a good game, good return. It changed when I served [on] the break point."
World No 47 Millman never stopped fighting, but the superior quality of Paire's serve – he banged down 13 aces – and his ability at the net ultimately made the difference.
Paire, who often rides an emotional rollercoaster on court, also seemed to release some tension towards the end of the first set, when he smashed his racquet in frustration.
"It can help me," agreed Paire. "The first set when I broke my racket honestly I was not feeling well the ball. I was a little bit nervous. In my mind it was not easy. So I said 'okay, destroy your racket and after you come back and play full'
"At the beginning I was a bit 50 per cent, pushing the ball into the middle of the court. So I said 'change everything, take another one, and maybe it will be better'."
Both players displayed tremendous court coverage in a gripping contest, and some of Paire's stop volleys had to be seen to be believed.
Paire also utilised the challenge system well, using hawkeye to overturn some crucial calls, particularly in the third set. It was a relief for the World No 24, who said he had been frustrated during his second round match on the outside court (where there is no hawkeye) with some calls.
"It helped me, but you never know with the challenge," said Paire.