The world number one is just the third player in the Open era after Jimmy Connors and Roger Federer to reach 10 consecutive quarter-finals at a single grand slam.
The Scot’s serve was broken three times by his French opponent, but each time he rallied to eventually secure a 7-6 (7/1) 6-4 6-4 victory.
Murray twice recovered from a break down to win the opening set on a tie-break.
A limp Paire service game in the second gave Murray an immediate break, but he was pegged back at 3-3 and saved four break points before clinching the set.
The world number one continued to limp, chuntered away angrily at his box and argued with the umpire as he struggled to find his timing.
But he grabbed the crucial break at 4-4 in the third set before serving out to seal his passage into the last eight.
There Murray will meet Sam Querrey, who came through the battle of the big serves in five sets on Court 18.
The American lost the first set 7-5 to South Africa’s Kevin Anderson, but levelled on a tie-break before taking the third with a rare break of serve.
A marathon tie-break in the fourth went Anderson’s way, after he survived four match points, but he was broken again in the decider as Querrey won 5-7 7-6 (7/5) 6-3 6-7 (11/13) 6-3.
Marin Cilic reached his fourth consecutive quarter-final with a straight-sets win over Roberto Bautista Agut.
The Croatian seventh seed overpowered his Spanish opponent in a one-sided contest, running out a 6-2 6-2 6-2 winner on Court 12.
Bautista Agut, seeded 18, had no answer to the fearsome groundstrokes of Cilic, one of the few men outside the top four to win a grand slam in recent years with his 2014 US Open victory.
The 28-year-old has never been beyond the last eight at these championships but looks every bit a threat to the big guns.