The 23-year-old dug deep in game five, though, battling back when faced with another break point to register his first game of the match with an overhead smash that the Scot, despite a determined effort, could not retrieve.
The remainder of the opener went with serve - but only just. Two lazy mistakes from Murray, indicative of what was to follow in the next set, gifted Monfils three break points at 5-2.
However, more Monfils sloppiness and two Murray aces eventually saw the Scot hold on to wrap up the first set.
But with the Frenchman finding his range on both his serves and his returns, and Murray's game inexplicably unravelling, the match turned on its head.
Monfils found himself 5-0 up and when a scampering Murray could not return an expertly placed drop-shot, the match was all square.
The momentum swung back in the world number four's favour again when he grittily emerged victorious in a thrilling rally that ended when Murray despatched into open court after a Boris Becker-like defensive dive from Monfils.
Not only was the retrieval futile in terms of the point, the world number 15's acrobatics also left him clutching his shoulder and wincing in pain during a brief consultation with the trainer after also losing the next game to go 2-0 down.
Monfils grimaces in pain as the trainer massages his shoulder in the final set
He soldiered on, though, to save two break points and claim the next game, before broke Murray once more to move within two games of victory at 4-2.
However, Murray again summoned his concentration to eventually grind out victory in two hours and five minutes and set up an intriguing last-eight clash against former world number three Nalbandian.
The 2002 Wimbledon finalist won the Legg Mason Classic in Washington on Sunday - his first event since injuring his hamstring in April. And he extended his winning streak to 11 matches with a 4-6 6-4 6-1 victory over fifth seed Swede Robin Soderling.
"Its a good victory for me, I feel that I'm playing well," reflected Argentine Nalbandian. "I'm going to try to keep going, I've been a long time out of the circuit. I'm enjoying my time now."
The 28-year-old has defeated Murray on the only two occasions they have met in the past.
Murray's SW19 debut in 2005 was ended by Nalbandian at the fourth-round stage in four sets and, in 2008, the world number 45 was again the victor - this time 7-6 6-3 at the Paris Masters.
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