The world number two had been superb in his first three matches but had to show his fighting qualities on Monday, particularly in the second set as he recovered from five games to two down and then 5-3 adrift in the tie-break.
Youzhny was a quarter-finalist here last year and is a talented grass-court player, but the third set was largely one-way traffic as Murray came through 6-4 7-6 (7/5) 6-1 to make the last eight, where he will meet Spain's Fernando Verdasco.
Murray's mantra throughout the fortnight has been not to look more than one round ahead, and he told the BBC: "I don't expect to come into these sort of events to win them, there's no guarantees.
"I've only won one. I'll just keep trying hard to keep winning. It gets harder as the tournament goes on.
"Serena Williams lost today, she doesn't lose particularly often. Roger (Federer) lost and Rafa (Nadal) lost. All these guys and girls are better players than me and have achieved a lot more than me so if they can lose, so can I."
The Scot was happy with the way he came through in the end today, saying: "It was a tough match, the first couple of sets especially.
"He also had a couple of chances at the start of the third set as well but once I got ahead in the third I concentrated very hard not to let him back in like I did in the second set.
"I just managed to turn the second set around in the breaker at the right moment. I came up with some good shots from 5-2 down."
Centre Court was still recovering from the shock of seeing Williams eliminated by Sabine Lisicki when Murray and Youzhny walked out.
The atmosphere was flat and so was the match in its early stages, with neither player finding their best form in the first set, although Murray secured the only break of serve in the third game.
It was all a struggle, though, and that continued in the second set, with Youzhny clawing his way back from 40-0 to deuce on Murray's serve in the second game.
Having come through that, Murray played two of his best shots of the match, a half-volley drop shot and pinpoint lob, to force a break point in the following game and then topped them both with a scrambling forehand pass.
But he could not cement it as Youzhny forced two break-back points, taking the second when Murray netted a forehand, the Scot slamming his racket into his shoe.
The situation was to get worse, as a few minutes later Murray double-faulted to hand Youzhny a second successive break and a 4-2 lead.
There was a nervousness around Centre Court, which only increased when Youzhny recovered from 0-30 to win a fourth game in a row.
Murray stopped the rot by holding, and with Youzhny serving for the set he got the crowd going with a brilliant forehand down the line on the stretch.
Two break points disappeared but a third arrived and this time Murray took it with a blistering cross-court backhand, geeing the crowd up as he ran back to his chair.
The 26-year-old had a chance to break for 6-5 but Youzhny landed a forehand right in the corner to hang on.
Murray was grabbing at his hip, perhaps a sign that his troublesome back was playing up, but he hammered down an ace to force a tie-break.
It was tense, and a tame double fault from Murray to trail 4-2 did not help, but he retrieved the mini-break with a precision drop shot, skipping into the air as he willed it over the net.
A forehand wide from Youzhny gave Murray his first set point, which he took in style with a stunning backhand return. The crowd roared and Murray yelled and punched the air.
Youzhny took a medical timeout before the start of the third set for treatment to his right shoulder, and immediately threatened the Murray serve once more.
There was confusion all round as Murray made a late decision to play a ball he thought was out, appealing to the line judge and umpire in vain.
That brought up a second break point but the Scot saved it with an ace and then took advantage of a poor game from his opponent to break to love for a 2-0 lead.
Youzhny's threat had passed, and another break gave Murray a 5-1 advantage and the chance to serve for it.
He set up a first match point with a sizzling forehand winner and put away a volley to clinch victory after two hours and 37 minutes.