Murray broke in the opening game and quickly moved 4-0 ahead and, despite a response from Chardy, took the opener 6-4.
From there on it was plain sailing for Murray as the next two sets flashed by, with the Brit completing a 6-4 6-1 6- victory.
Read below how the action unfolded with Sports Mole's live commentary.
4.56amHello again. We're about to see the third quarter-final of the day, and the penultimate one overall. It's the third men's quarter between Andy Murray and Jeremy Chardy.
4.59amIt's 22 degrees out there on court. Much more pleasant conditions than earlier in the week that saw Gilles Simon taken to hospital.
5amThe Frenchman did recover to face Murray in the last round but was comprehensively beaten by the third seed in straight sets.
5.02amMurray is the red hot favourite for this one, as you might expect. But he shouldn't underestimate the Frenchman, as he has beaten Juan Martin del Potro and Andreas Seppi, both of whom were favourites over him.
5.04amThe winner of this one will meet the winner of the last quarter-final tonight, which is scheduled for a start not before 8.30am. The players in action? Roger Federer and Jo-Wilfried Tsonga.
5.05amThe warm-up hits are over and we're about ready to get started.
5.06amPoor start from the Frenchman. Two errors and he's 0-30 down.
5.07amAn early glimpse of the Chardy forehand, followed by an ace, brings him level.
Chardy 0-1* MurrayBREAK! The Frenchman goes back to the poor after those two shots and Murray without really doing anything! Chardy compounds his dreadful start with a point-blank volley into the net.
5.11amChardy hits his third forehand winner to move 15-30 ahead.
5.12amMurray hits a forehand into the net and Chardy has an immediate chance to break back.
Chardy *0-2 MurrayMurray saves the break point and controls the rest of his service game to hold in his opener. Some nervy moments but good play to recover. The break is consolidated.
5.17amBrilliant from Murray at 30-15 down. He works the angles to finish with an inside-out forehand right into the corner.
Chardy 0-3* MurrayBREAK! The same shot brings up a break point for Murray; he's not afraid to aim towards that Chardy forehand. Great play again brings Murray to the net and he volleys the winner for another break. He's cruising.
5.21amSolid serving takes Murray into a 30-0 lead.
Chardy *0-4 MurrayMurray does put a poor one into the net but aside from that it's plain sailing on his serve and after 17 minutes Murray is four games up.
Chardy 1-4* MurrayMurray almost pulls of the shot of the tournament so far with a backhand deep into the shadows, but Chardy finds his range and opens his account for the match with a huge ace down the middle.
5.29amChardy has come alive, he now has three break points after a good rally.
Chardy *2-4 MurrayBREAK! Chardy gets one back! He breaks to love with a combination of excellent, accurate hitting and poor shots from Murray.
5.32amChardy is running Murray ragged just now. Eight straight points now.
Chardy 3-4* MurrayFrom 4-0 down Chardy is now just one behind. However, Murray does still have a break. Chardy finishes the last game with another excellent forehand that Murray cannot get back.
5.35amCan Chardy get more success here on the Murray serve to level the match?
5.37amIt's a battle out there, and one that Chardy is edging. Another big forehand cannot be returned and it's 15-30.
Chardy *3-5 MurrayMurray had to dig deep there but he recovers to hold with a swerving ace down the middle. Chardy was expecting it wide and got himself way out of position. One game now for Murray to take the opener.
5.40amChardy looks for a lob after Murray advances, but hits it long.
Chardy 4-5* MurrayHowever, Chardy responds to force Murray to serve for the set. Winning four games after being 4-0 down is a good effort, and suggests that he could be well in the second set should he lose this one.
5.44amIf he loses this one... He's still in this set as he gets to 0-30.
5.46amFantastic serving from Murray to turn it around. He now has a set point at 40-30.
Chardy *4-6 MurraySET! It wasn't as comfortable as it looked after 17 minutes of the set, but Murray does take it and that will be a big boost. Chardy came into the set after being 4-0 down so will surely make the second a close-fought contest.
5.52amChardy will need to hold his first few games of this set to get back into it. He currently leads 30-15.
Chardy 4-6 1-0* MurrayHe finishes with a good, wide ace and does indeed hold first up. It's already a better set than his first one. Can he now attack the Murray serve?
5.55amA smash and a big serve move the Brit to 30-0.
Chardy 4-6 *1-1 MurrayYou can't ask for any more than a comfortable hold to love. It puts the pressure right back on Chardy, especially with the luck he got clipping the top of the net with a volley to win the game.
5.57amChardy twice goes wide to the right-hand tramlines and Murray has a look-in here at 0-30.
Chardy 4-6 1-2* MurrayBREAK! Superb lob from deep sets up three break points and he converts his third from three attempts to break to love. Very strong start to this set from Murray.
6.05amMurray moves 0-30 ahead, but Chardy responds with a booming ace down the middle.
6.06amPoor forehand from Chardy goes wide, and Murray has another break point.
Chardy 4-6 1-4* MurrayBREAK! He converts four from four and gets another double break, just as he did in the last set. He will want to hang on better than he managed last time though. This is looking a bit routine now.
6.11amChardy moves into a 0-30 lead. Murray gets the vital fourth point but then poorly hits the net to give away two break points.
6.12amAbsolutely superb from Murray. He defends brilliantly before switching to attack mode and finishing with a glorious passing forehand.
6.13amHe's saved the second break point, too, with another defensive effort. He owes a lot to Chardy hitting the net from right on top of it, however.
Chardy 4-6 *1-5 MurrayComing back from 15-40 shows the difference between the players at the top and the rest. Chardy digs his heels in with a few deuces but Murray takes a big hold with two huge aces in a row.
6.18amBig forehand hits the line form Murray to go 30-0 ahead. He wants this set on Chardy's serve.
6.19amOne is saved with a good cross-court forehand.
Chardy 4-6 1-6* MurraySET! Chardy saves another but a terrible double fault - the second after throwing the ball up well behind him and going long - gifts Murray the second set.
6.23amThat was all too easy for Murray. Chardy has shown the odd big forehand and serve, but not nearly enough overall. It's a long way back from here.
Chardy 4-6 1-6 *0-1 MurrayThere's a sense that Chardy has given up the ghost here. He's offering no resistance to the Murray serve and a routine hold to love for Murray brings up the first of the set. Perfect start to the third.
6.28amMurray has missed a few backhands today, and another one into the net gives Chardy a 30-15 lead in this game.
Chardy 4-6 1-6 0-2* MurrayBREAK! Murray steps into the Chardy second serve and works the point so he can finish with a booming forehand and the Frenchman nets for an immediate break for the Brit.
6.31amIf you're already looking forward to tomorrow's semi-finals, take a look at the order of play.
Chardy 4-6 1-6 *0-3 MurrayChardy digs in a bit, but Murray is just too strong and holds well from 15-30 down. It's been some time since Chardy won a game.
6.36amAn ace and a one-two forehand down the line moves Chardy 30-0 up. Great tennis from him, but Murray responds with an unbelievable forehand from deep that clips the line past the Frenchman.
6.37amWow. That is some shot. Murray races down an attempted drop shot and powers a forehand back past Chardy. We're starting to see the best of Murray in this one.
Chardy 4-6 1-6 1-3* MurrayChardy is still battling, which is good. He saved a couple of break points to claim his first game of the third set.
Chardy 4-6 1-6 *1-4 MurrayAgain, not much resistance from Chardy on the Murray serve. Chardy goes long in a tired rally before Murray takes the game with a fine cross-court forehand.
6.46amChardy can't quite chase a drop shot from Murray, which wasn't one of his best, and puts his return into the net.
6.47amMurray chases a lob and somehow scoops it back into play. However he goes millimetres wide with the next forehand.
Chardy 4-6 1-6 1-5* MurrayBREAK! Brilliant break from Murray. He attacks the Chardy serve on the last point, sending him right then left before finishing up at the net. Superb all-round tennis from the third seed. He'll serve for the match now.
Chardy 4-6 1-6 *2-5 MurrayBREAK! Well, I didn't see that coming! Murray double faults to gift Chardy a break point, and he then slaps one into the net. He'll have to wait for his place in the semis. Really poor.
6.54amHe's missing all his shots now Murray. This time a forehand goes into the tramlines for 30-0.
6.55amA bit nervy at the net from Murray, but he responds with a controlled smash.
Chardy 4-6 1-6 2-6 MurrayGAME, SET AND MATCH! Chardy drifts out of the game again after the last break and almost finds the crowd with a forehand. Murray gets the win and it was a good performance, his best so far certainly.
6.57amSo Murray goes through to face Federer or Tsonga, which is up next at about 8.30am. Should be a belter!
6.58amThanks for joining me today! Please stay with us for that Federer clash. The commentary will be up on site in about an hour.