Johanna Konta fulfilled her end of the bargain against Caroline Garcia and Murray ensured there was no upset on Centre Court with a 7-6 (7/1) 6-4 6-4 triumph.
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.
But this was not Murray at his best and questions remain about his fitness despite the Scot attempting to play down any concern over a hip problem.
Following on from Alexander Bublik, Dustin Brown and Fabio Fognini, Paire is another of the tour's more quirky characters, and Murray may simply be desperately short of rhythm.
Frenchman Paire, ranked 46, is known for his backhand, temper, drop shots and all-round unpredictability.
He launched himself into the air to play shots several times - never successfully - and hit 50 winners to Murray's 25.
But he also made 44 unforced errors to just eight from his opponent, and ultimately did not come close to denying the home favourite.
The victory continued Murray's remarkable record against players from across the Channel - it is close to a decade and 28 matches since he lost to a Frenchman at a grand slam.
Next he will play Sam Querrey from the United States, who defeated South Africa's Kevin Anderson 5-7 7-6 (7/5) 6-3 6-7 (11/13) 6-3 shortly after Murray celebrated his own victory.
The defending champion had made fast starts in all his first three matches but this time he found himself behind after only three games.
The world number one, who continued to limp, was struggling with his timing and was on the wrong end of three straight breaks as Paire moved into a 4-2 lead.
But the Frenchman is about as reliable as Wimbledon weather, and a wild drive volley and poor forehand allowed Murray to pull level.
Paire saved two set points to force a tie-break only to lose the first six points, and then dropped serve immediately at the start of the second set.
He dialled back in again in the sixth game and broke back but Murray at last found a flashing backhand winner to force another break and a chance to serve for the set.
The world number one may not have been at his best but, as ever, he was fighting and he saved four break points before clinching it.
The tension had dissipated, and Murray at last began to look a little more comfortable.
He probed away at the Paire serve and got his reward in the ninth game with a break that left him serving for the match.
This time there were no problems for Murray as a Paire forehand dropped long on his first match point to give the Scot victory after two hours and 21 minutes.
Murray was happy with his performance and felt it was a step up from his previous matches.
He told the BBC: "I thought I played well today apart from a couple of sloppy service games in the first set. That's by far the best I have hit it this week. He's not an easy guy to play, tactics aren't easy against him."
Of his hip problems, Murray added: "Two weeks ago I was resting and a bit concerned, it was frustrating. But I have managed it well and have played some good stuff. I'm doing well and hopefully will keep it up."
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