Murray did not have it all his own way against the Frenchman, but he did enough to come through by a 7-6 6-4 6-4 scoreline.
Twice during the opening set, the world number one found himself a break of serve behind to a player who had recorded his best-ever performance at SW19, but Murray dominated the tie-break to seize control of the match.
It remained a tight affair during the second as Paire’s variety troubled Murray but the two-time champion played the big points well and was eventually able to extend his lead.
Paire showed no signs of wilting and forced Murray to dig deep in order to remain competitive in the third but after breaking in the ninth game, Murray was able to serve the contest out to secure victory in two hours and 21 minutes.
He will now face American Sam Querrey in the last eight.