Despite progressing in straight sets, Murray’s victory was far from straightforward, with Paire’s tendency to attempt the ambitious occasionally bearing fruit and testing the world number one.
Defending champion Murray - who became just the third man to reach the quarter-finals in 10 successive years at a grand slam event - will face Sam Querrey or Kevin Anderson in the last eight.
Having won his third-round clash in a dramatic fourth set against Fabio Fognini, Murray could have done with getting off to a smooth start.
However, Paire’s unpredictable style caused the Scot problems early on and two early drops of serve - either side of a break of his own - had Murray berating himself and shouting to his box.
Murray soon settled and got the match back on an equal footing with a break in the eighth game but he was forced into a tie-break after failing to convert two set points on the Paire serve.
If the set itself was tight, the tie-break was anything but - Paire opened with a double fault on his way to a 7-1 drubbing.
Paire’s woes continued into the second set when he was broken to love in the opening game, but he restored parity at 3-3 after getting that disappointment out of his system.
A stunning backhand and a wonderfully returned drop shot helped Murray to what promised to be the set-clinching break, and the top seed did - at the fifth time of asking - open up a 2-0 advantage in the next game.
To come away from two tight sets against the world number one empty-handed will have been tough for Paire to take, and the world number 46 was made to rue a double fault - one of 10 in the match compared to none from Murray - that took the ninth game to deuce, with Murray eventually making the break.
That left Murray serving for the match and he sealed victory thanks to a long Paire forehand, extending his winning run against French opponents to 26.
STATISTICAL BREAKDOWNMurray [1] bt Paire 7-6 (7-1) 6-4 6-4
WINNERS/UNFORCED ERRORSMurray - 25/8Paire - 50/44
ACES/DOUBLE FAULTSMurray - 4/0Paire - 9/10
BREAK POINTS WONMurray - 5/16Paire - 3/11
FIRST SERVE PERCENTAGEMurray - 71Paire - 54
PERCENTAGE OF POINTS WON ON FIRST/SECOND SERVEMurray - 67/69Paire - 65/44
TOTAL POINTSMurray - 123Paire - 100
0 votes