He now faces Roger Federer for the chance to reach his second consecutive Grand Slam final.
The world number three was in control early on, before having to withstand a fightback from an opponent who appeared initially nervous on his first appearance in the last eight of a grand slam.
Murray said after his 6-4, 6-1, 6-2 victory: "Today was the best I have played. I have struggled in the last few rounds, Jeremy has had a great tournament and beat some good players, so I had to start well."
Murray made a strong start, taking the opening set in 44 minutes. The Frenchman tossed in two double faults in the opening game and then netted a high backhand volley on break point to gift the Scot the initiative.
Chardy came into this match having hit the most forehand winners in the tournament and it was no surprise that Murray continually probed the backhand in the early exchanges.
It was proving a smart tactic as another weak shot off that side at 0-2, 30-40 allowed Murray a simple volley and left him a double break to the good.
A booming ace finally got Chardy on the board before he got one of the breaks back as Murray netted a routine sliced backhand of his own.
Chardy was finally starting to warm to his task but, despite getting to deuce with Murray serving for the set, he could not find a way through as the US Open champion edged in front.
Chardy won their most recent meeting at the Cincinnati Masters last year but he found himself in deeper trouble at the start of the second set as Murray capitalised on some wild shots from the world number 36 to establish a 3-1 lead.
And with Chardy struggling with his ball toss, it was no surprise when Murray broke for a fourth time in the match to move further ahead.
But as he did in the first set, he took his foot off the pedal.
This time, however, he was able to dig himself out of the hole thanks to some wonderful defence.
Serving at 4-1, Murray slipped 15-40 down but saved the first break point with a crisp passing forehand having been moved round the court and the second after some wonderful baseline scrambling prompted Chardy to dump a routine volley into the net.
He managed to hold for 5-1 and then broke again with Chardy beginning to look disheartened.
Murray had not lost from two sets up since going down to David Nalbandian at Wimbledon in 2005.
And a comeback never looked likely here with Chardy's game starting to disintegrate.
He was broken once more after putting a weak forehand in the net to hand Murray a 2-0 lead.
The third seed saw another break-point chance come and go for 4-0 before Chardy held, but it mattered little as a beautifully constructed point saw Murray surge 5-1 ahead.
There was a minor blip when he failed to serve it out at the first attempt as his concentration wavered, but he promptly claimed the match in the next game to win in one hour and 51 minutes.